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We construct the first four-dimensional multi-black hole solution of general relativity with a positive cosmological constant. The solution consists of two static black holes whose gravitational attraction is balanced by the cosmic expansion. These static binaries provide the first four-dimensional example of non-uniqueness in general relativity without matter., Comment: 15 pages, 8 figures. v2: matches published version (improved discussions and Figs. 6 and 7 added)

Stephen Hawking's contributions to the understanding of gravity, black holes and cosmology were truly immense. They began with the singularity theorems in the 1960s followed by his discovery that black holes have an entropy and consequently a finite temperature. Black holes were predicted to emit thermal radiation, what is now called Hawking radiation. He pioneered the study of primordial black holes and their potential role in cosmology. His organisation of and contributions to the Nuffield Workshop in 1982 consolidated the picture that the large-scale structure of the universe originated as quantum fluctuations during the inflationary era. Work on the interplay between quantum mechanics and general relativity resulted in his formulation of the concept of the wavefunction of the universe. The tension between quantum mechanics and general relativity led to his struggles with the information paradox concerning deep connections between these fundamental areas of physics. These achievements were all accomplished following the diagnosis during the early years of Stephen's studies as a post-graduate student in Cambridge that he had incurable motor neuron disease -- he was given two years to live. Against all the odds, he lived a further 55 years. The distinction of his work led to many honours and he became a major public figure, promoting with passion the needs of disabled people. His popular best-selling book A Brief History of Time made cosmology and his own work known to the general public worldwide. He became an icon for science and an inspiration to all., Comment: 38 pages

Electromagnetism in spacetime can be treated in terms of an analogue linear dielectric medium. In this paper, we discuss the gravitational analogue of the linear magnetoelectric effect, which can be found in multiferroic materials. While this is known to occur for metrics with non-zero mixed components, we show how it depends on the choice of spatial formalism for the electromagnetic fields, including in differences in tensor weight, and also on the choice of coordinate chart. This is illustrated for Langevin-Minkowski, four charts of Schwarzschild spacetime, and two charts of pp gravitational waves., Comment: 13 pages

We show that, contrary to what is usually claimed in the literature, the zero mass limit of Kerr spacetime is not flat Minkowski space but a spacetime whose geometry is only locally flat. This limiting spacetime, as the Kerr spacetime itself, contains two asymptotic regions and hence cannot be topologically trivial. It also contains a curvature singularity, because the power-law singularity of the Weyl tensor vanishes in the limit but there remains a distributional contribution of the Ricci tensor. This spacetime can be interpreted as a wormhole sourced by a negative tension ring. We also extend the discussion to similarly interpret the zero mass limit of the Kerr-(anti)-de Sitter spacetime., Comment: 14 pages, 4 figures, references added

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial data set $(\Sigma, h_{ij}, K_{ij})$ admitting a suitably defined convex function. We show how the existence of a convex function on a spacetime places restrictions on the properties of the spacetime geometry., Comment: In the light of recent renewed interest in this topic (see arxiv: 1510.04228 and 1702.02652) we are submitting this brief summary of our old results presented by A.I. at the International Workshop: Frontiers of Cosmology and Gravitation held in Kyoto in 2001.and published in the proceedings. See also arXiv:gr-qc/0011055

We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescaling them and extending to complex parameter values yields axially symmetric vacuum solutions containing conical singularities along circles that can be viewed as singular matter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings literally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality transformations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for example the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts along the symmetry axes, apart from solutions with locally flat geometry., Comment: 42 pages, 9 figures, added references and an appendix discussing the Flamm embedding versus Einstein-Rosen bridge; matches the published version

We apply duality rotations and complex transformations to the Schwarzschild metric to obtain wormhole geometries with two asymptotically flat regions connected by a throat. In the simplest case these are the well-known wormholes supported by phantom scalar field. Further duality rotations remove the scalar field to yield less well known vacuum metrics of the oblate Zipoy-Voorhees-Weyl class, which describe ring wormholes. The ring encircles the wormhole throat and can have any radius, whereas its tension is always negative and should be less than $-c^4/4G$. If the tension reaches the maximal value, the geometry becomes exactly flat, but the topology remains non-trivial and corresponds to two copies of Minkowski space glued together along the disk encircled by the ring. The geodesics are straight lines, and those which traverse the ring get to the other universe. The ring therefore literally produces a hole in space. Such wormholes could perhaps be created by negative energies concentrated in toroidal volumes, for example by vacuum fluctuations., Comment: matches the published version

In this work a series of methods are developed for understanding the Friedmann equation when it is beyond the reach of the Chebyshev theorem. First it will be demonstrated that every solution of the Friedmann equation admits a representation as a roulette such that information on the latter may be used to obtain that for the former. Next the Friedmann equation is integrated for a quadratic equation of state and for the Randall--Sundrum II universe, leading to a harvest of a rich collection of new interesting phenomena. Finally an analytic method is used to isolate the asymptotic behavior of the solutions of the Friedmann equation, when the equation of state is of an extended form which renders the integration impossible, and to establish a universal exponential growth law., Comment: 40 pages, no figures

In certain circumstances tools of Riemannian geometry are sufficient to address questions arising in the more general Finslerian context. We show that one such instance presents itself in the characterisation of geodesics in Randers spaces of constant flag curvature. To achieve a simple, Riemannian derivation of this special family of curves, we exploit the connection between Randers spaces and the Zermelo problem of time-optimal navigation in the presence of background fields. The characterisation of geodesics is then proven by generalising an intuitive argument developed recently for the solution of the quantum Zermelo problem., Comment: 9 pages, published version

This paper is a continuation of our earlier study on the integrability of the Friedmann equations in the light of the Chebyshev theorem. Our main focus will be on a series of important, yet not previously touched, problems when the equation of state for the perfect-fluid universe is nonlinear. These include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born--Infeld, and two-fluid models. We show that some of these may be integrated using Chebyshev's result while other are out of reach by the theorem but may be integrated explicitly by other methods. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution. For example, in the Chaplygin gas universe, it is seen that, as far as there is a tiny presence of nonlinear matter, linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics not directly related to cosmology. We provide some examples ranging from geometric optics and central orbits to soap films and the shape of glaciated valleys to which our results may be applied., Comment: 43 pages no figures

We study the thermodynamical properties of a class of asymptotically conical (AC) geometries known as "subtracted geometries". We derive the mass and angular momentum from the regulated Komar Integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other AC geometries., Comment: 5p, presentation improved, version to appear in Physical Review Letters

We study the vacuum polarization of a massless minimally coupled scalar field at the horizon of four-charge STU black holes. We compare the results for the standard asymptotically flat black holes and for the black holes obtained in the "subtracted limit", both in the general static case and at the horizon pole for the general rotating case. The original and the subtracted results are identical only in the BPS limit, and have opposite sign in the extremal Kerr limit. We also compute the vacuum polarization on the static solutions that interpolate between both the original and the subtracted case through a solution-generating transformation and show that the vacuum polarization stays positive throughout the interpolating solution. In the Appendix we provide a closed-form solution for the Green's function on general (static or rotating) subtracted black hole geometries., Comment: 22 pages, 2 figures

The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By lifting the problem from the state space to the space of unitary gates realising the required task, we are able to deduce the form of the solution to the problem by deriving a universal quantum speed limit. The expression thus obtained indicates that further simplifications of this apparently difficult problem are possible if we switch to the interaction picture of quantum mechanics. A complete solution to the navigation problem for an arbitrary quantum system is then obtained, and the behaviour of the solution is illustrated in the case of a two-level system., Comment: 7 pages, 4 figures; version to appear in New Journal of Physics

This short but systematic work demonstrates a link between Chebyshev's theorem and the explicit integration in cosmological time $t$ and conformal time $\eta$ of the Friedmann equations in all dimensions and with an arbitrary cosmological constant $\Lambda$. More precisely, it is shown that for spatially flat universes an explicit integration in $t$ may always be carried out, and that, in the non-flat situation and when $\Lambda$ is zero and the ratio $w$ of the pressure and energy density in the barotropic equation of state of the perfect-fluid universe is rational, an explicit integration may be carried out if and only if the dimension $n$ of space and $w$ obey some specific relations among an infinite family. The situation for explicit integration in $\eta$ is complementary to that in $t$. More precisely, it is shown in the flat-universe case with $\Lambda\neq0$ that an explicit integration in $\eta$ can be carried out if and only if $w$ and $n$ obey similar relations among a well-defined family which we specify, and that, when $\Lambda=0$, an explicit integration can always be carried out whether the space is flat, closed, or open. We also show that our method may be used to study more realistic cosmological situations when the equation of state is nonlinear., Comment: Extended and re-organized version to appear in JCAP

In a previous paper [arXiv:1308.1852] we showed how a finite system of discrete particles interacting with each other via Newtonian gravitational attraction would lead to precisely the same dynamical equations for homothetic motion as in the case of the pressure-free Friedmann-Lema\^{i}tre-Robertson-Walker cosmological models of General Relativity Theory, provided the distribution of particles obeys the central configuration equation. In this paper we show one can obtain perturbed such Newtonian solutions that give the same linearised structure growth equations as in the general relativity case. We also obtain the Dmitriev-Zeldovich equations for subsystems in this discrete gravitational model, and show how it leads to the conclusion that voids have an apparent negative mass., Comment: 24 pages

Starting from the geometrical concept of a 4-dimensional de-Sitter configuration of spheres in Euclidean 3-space and modelling voids in the Universe as spheres, we show that a uniform distribution over this configuration space implies a power-law for the void number density which is consistent with results from the excursion set formalism and with data, for an intermediate range of void volumes. The scaling dimension of the large scale structure can be estimated as well. We also discuss the effect of restricting the survey geometry on the void statistics. This work is a new application of de-Sitter geometry to cosmology and also provides a new geometrical perspective on self-similarity in cosmology., Comment: 8 pages, 4 figures, accepted by MNRAS. Minor changes, appendix added

In this paper we lay down the foundations for a purely Newtonian theory of cosmology, valid at scales small compared with the Hubble radius, using only Newtonian point particles acted on by gravity and a possible cosmological term. We describe the cosmological background which is given by an exact solution of the equations of motion in which the particles expand homothetically with their comoving positions constituting a central configuration. We point out, using previous work, that an important class of central configurations are homogeneous and isotropic, thus justifying the usual assumptions of elementary treatments. The scale factor is shown to satisfy the standard Raychaudhuri and Friedmann equations without making any fluid dynamic or continuum approximations. Since we make no commitment as to the identity of the point particles, our results are valid for cold dark matter, galaxies, or clusters of galaxies. In future publications we plan to discuss perturbations of our cosmological background from the point particle viewpoint laid down in this paper and show consistency with much standard theory usually obtained by more complicated and conceptually less clear continuum methods. Apart from its potential use in large scale structure studies, we believe that out approach has great pedagogic advantages over existing elementary treatments of the expanding universe, since it requires no use of general relativity or continuum mechanics but concentrates on the basic physics: Newton's laws for gravitationally interacting particles., Comment: 33 pages; typos fixed, references added, some clarifications

The cumulative size-frequency distributions of impact craters on planetary bodies in the solar system appear to approximate a universal inverse square power-law for small crater radii. In this article, we show how this distribution can be understood easily in terms of geometrical statistics, using a de-Sitter geometry of the configuration space of circles on the Euclidean plane and on the unit sphere. The effect of crater overlap is also considered., Comment: 6 pages, 2 figures, accepted by MNRAS. Version 2: title modified, appendix added, some small changes

An exact solution representing black holes in an expanding universe is found. The black holes are maximally charged and the universe is expanding with arbitrary equation of state. It is an exact solution of the Einstein-scalar-Maxwell system, in which we have two Maxwell-type U(1) fields coupled to the scalar field. The potential of the scalar field is an exponential. We find a regular horizon, which depends on one parameter (the ratio of the energy density of U(1) fields to that of the scalar field). The horizon is static because of the balance on the horizon between gravitational attractive force and U(1) repulsive force acting on the scalar field. We also calculate the black hole temperature., Comment: 4 pages, 1 table, 2 figures

Generalizing previous work by two of us, we prove the non-existence of certain stationary configurations in General Relativity having a spatial reflection symmetry across a non-compact surface disjoint from the matter region. Our results cover cases such that of two symmetrically arranged rotating bodies with anti-aligned spins in $n+1$ ($n \geq 3$) dimensions, or two symmetrically arranged static bodies with opposite charges in 3+1 dimensions. They also cover certain symmetric configurations in (3+1)-dimensional gravity coupled to a collection of scalars and abelian vector fields, such as arise in supergravity and Kaluza-Klein models. We also treat the bosonic sector of simple supergravity in 4+1 dimensions., Comment: 13 pages; slightly amended version, some references added, matches version to be published in Classical and Quantum Gravity

We study a system of N D3-branes in which open string tachyons survive in the low energy alpha' -> 0 limit. We compute the height of the tachyon potential both in the weak and strong couplings by using N=4 super Yang-Mills and the dual AdS_5 descriptions respectively. We find an exact agreement between the two descriptions in the large N limit. This provides an example of gravitational duals of open string tachyon condensation., Comment: 4 pages, v2: references and footnotes added

Minimal surfaces and domain walls play important roles in various contexts of spacetime physics as well as material science. In this paper, we first review the Bernstein conjecture, which asserts that a plane is the only globally well defined solution of the minimal surface equation which is a single valued graph over a hyperplane in flat spaces, and its failure in higher dimensions. Then, we review how minimal cones in four- and higher-dimensional spacetimes, which are curved and even singular at the apex, may be used to provide counterexamples to the conjecture. The physical implications of these counterexamples in curved spacetimes are discussed from various points of view, ranging from classical general relativity, brane physics, and holographic models of fundamental interactions., Comment: 19 pages, no figure; v2: comments added in footnote 1 and 2

We argue that the natural framework for embedding the ideas of deformed, or doubly, special relativity (DSR) into a curved spacetime is a generalisation of Einstein-Cartan theory, considered by Stelle and West. Instead of interpreting the noncommuting "spacetime coordinates" of the Snyder algebra as endowing spacetime with a fundamentally noncommutative structure, we are led to consider a connection with torsion in this framework. This may lead to the usual ambiguities in minimal coupling. We note that observable violations of charge conservation induced by torsion should happen on a time scale of 10^3 s, which seems to rule out these modifications as a serious theory. Our considerations show, however, that the noncommutativity of translations in the Snyder algebra need not correspond to noncommutative spacetime in the usual sense., Comment: 20 pages, 1 figure, revtex; expanded sections 3 and 4 for clarity, moved material to appendix B, corrected a few minor errors

We address the problem of the apparently very small magnitude of CP violation in the standard model, measured by the Jarlskog invariant J. In order to make statements about probabilities for certain values of J, we seek to find a natural measure on the space of Kobayashi-Maskawa matrices, the double quotient U(1)^2\SU(3)/U(1)^2. We review several possible, geometrically motivated choices of the measure, and compute expectation values for powers of J for these measures. We find that different choices of the measure generically make the observed magnitude of CP violation appear finely tuned. Since the quark masses and the mixing angles are determined by the same set of Yukawa couplings, we then do a second calculation in which we take the known quark mass hierarchy into account. We construct the simplest measure on the space of 3 x 3 Hermitian matrices which reproduces this known hierarchy. Calculating expectation values for powers of J in this second approach, we find that values of J close to the observed value are now rather likely, and there does not seem to be any fine tuning. Our results suggest that the choice of Kobayashi-Maskawa angles is closely linked to the observed mass hierarchy. We close by discussing the corresponding case of neutrinos., Comment: 40 pages, 3 figures, corrected references, cited figures etc., no substantial changes in content

We construct a natural measure on the space of CKM matrices in the standard model, assuming the fermion mass matrices are randomly selected from a distribution which fits the observed quark mass hierarchy. This measure allows us to assess the likelihood of Jarlskog's CP violation parameter J taking its observed value J $\approx$ 3 x 10^{-5}. While well below the mathematically allowed maximum, we find that this value is in fact typical, once the observed quark masses are assumed., Comment: 4 pages; corrected minor errors, added discussion of the work of Donoghue et al

The Petrov solution (for $\Lambda=0$) and the Kaigorodov-Ozsv\'ath solution (for $\Lambda<0$) provide examples of vacuum solutions of the Einstein equations with simply-transitive isometry groups. We calculate the boundary stress-tensor for the Kaigorodov-Ozsv\'ath solution in the context of the adS/CFT correspondence. By giving a matrix representation of the Killing algebra of the Petrov solution, we determine left-invariant one-forms on the group. The algebra is shown to admit a two-parameter family of linear deformations a special case of which gives the algebra of the Kaigorodov-Ozsv\'ath solution. By applying the method of non-linear realisations to both algebras, we obtain a Lagrangian of Finsler type from the general first-order action in both cases. Interpreting the Petrov solution as the exterior solution of a rigidly rotating dust cylinder, we discuss the question of creation of CTCs by spinning up such a cylinder. We show geodesic completeness of the Petrov and Kaigorodov-Ozsv\'ath solutions and determine the behaviour of geodesics in these spacetimes. The holonomy groups were shown to be given by the Lorentz group in both cases., Comment: 25 pages (latex), 3 figures, corrected a few minor errors

We investigate the intermediate and late-time behaviour of the massive Dirac spinor field in the background of static spherically symmetric brane-world black hole solutions. The intermediate asymptotic behaviour of the massive spinor field exhibits a dependence on the field's parameter mass as well as the multiple number of the wave mode. On the other hand, the late-time behaviour power law decay has a rate which is independent of those factors., Comment: RevTex 8 pages, to be published in Phys.Rev.D15

The intermediate and late-time behaviour of a massive Dirac field in the background of static spherically symmetric black hole solutions is investigated. The intermediate asymptotic behaviour of a massive Dirac field depends on the mass parameter as well as the wave number of the mode, while the late time behaviour has a power law decay rate independent of both., Comment: RevTex, 8 pages, to be published in Phys.Rev.D15

We show how, in heterotic M-theory, an M5-brane in the 11-dimensional bulk may end on an ``M9-brane'' boundary, the M5-brane boundary being a Yang monopole 4-brane. This possibility suggests various novel 5-brane configurations of heterotic M-theory, in particular a static M5-brane suspended between the two M9-brane boundaries, for which we find the asymptotic heterotic supergravity solution., Comment: 4 pages, 3 figures, version to appear in PRL

Some speculative preliminary ideas relating matrix theory and cosmology are discussed., Comment: 17 pages. Slightly extended version of the talk given by G. W. Gibbons at the Mitchell Institute Conference on Cosmology; v2: references added

We study the linearised stability of the nakedly singular negative mass Schwarzschild solution against gravitational perturbations. There is a one parameter family of possible boundary conditions at the singularity. We give a precise criterion for stability depending on the boundary condition. We show that one particular boundary condition is physically preferred and show that the spacetime is stable with this boundary condition., Comment: 20 pages. 5 figures

The volumes, spectra and geodesics of a recently constructed infinite family of five-dimensional inhomogeneous Einstein metrics on the two $S^3$ bundles over $S^2$ are examined. The metrics are in general of cohomogeneity one but they contain the infinite family of homogeneous metrics $T^{p,1}$. The geodesic flow is shown to be completely integrable, in fact both the Hamilton-Jacobi and the Laplace equation separate. As an application of these results, we compute the zeta function of the Laplace operator on $T^{p,1}$ for large $p$. We discuss the spectrum of the Lichnerowicz operator on symmetric transverse tracefree second rank tensor fields, with application to the stability of Freund-Rubin compactifications and generalised black holes., Comment: 1+43 pages, 2 figures, LaTeX. Minor typos corrected

It has been believed that topology and signature change of the universe can only happen accompanied by singularities, in classical, or instantons, in quantum, gravity. In this note, we point out however that in the braneworld context, such an event can be understood as a classical, smooth event. We supply some explicit examples of such cases, starting from the Dirac-Born-Infeld action. Topology change of the brane universe can be realised by allowing self-intersecting branes. Signature change in a braneworld is made possible in an everywhere Lorentzian bulk spacetime. In our examples, the boundary of the signature change is a curvature singularity from the brane point of view, but nevertheless that event can be described in a completely smooth manner from the bulk point of view., Comment: 26 pages, 8 figures, references and comments are added, minor revisions and a number of additional footnotes added, error corrected, minor corrections, to appear in Class. Quant. Grav

We prove the uniqueness of higher dimensional (dilatonic) charged black holes in static and asymptotically flat spacetimes for arbitrary vector-dilaton coupling constant. An application to the uniqueness of a wide class of black p-branes is also given., Comment: 6 pages

We prove a uniqueness theorem for asymptotically flat static charged dilaton black hole solutions in higher dimensional space-times. We also construct infinitely many non-asymptotically flat regular static black holes on the same space-time manifold with the same spherical topology. An application to the uniqueness of a certain class of flat $p$-branes is also given., Comment: 4 pages

We prove the uniqueness theorem for asymptotically flat static vacuum black hole solutions in higher dimensional space-times. We also construct infinitely many non-asymptotically flat regular static black holes on the same spacetime manifold with the same spherical topology., Comment: to appear in Progress of Theoretical Physics Supplement No. 148

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial data set $(\Sigma, h_{ij}, K_{ij})$ admitting a suitably defined convex function. We show how the existence of a convex function on a spacetime places restrictions on the properties of the spacetime geometry., Comment: 26 pages, latex, 7 figures, improved version. some claims removed, references added

We study non-linear electrodynamics in curved space from the viewpoint of dualities. After establishing the existence of a topological bound for self-dual configurations of Born-Infeld field in curved space, we check that the energy-momentum tensor vanishes. These properties are shown to hold for general duality-invariant non-linear electrodynamics. We give the dimensional reduction of Born-Infeld action to three dimensions in a general curved background admitting a Killing vector. The SO(2) duality symmetry becomes manifest but other symmetries present in flat space are broken, as is U-duality when one couples to gravity. We generalize our arguments on duality to the case of n U(1) gauge fields, and present a new Lagrangian possessing SO(n) X SO(2)_elemag duality symmetry. Other properties of this model such as Legendre duality and enhancement of the symmetry by adding dilaton and axion, are studied. We extend our arguments to include a background b-field in the curved space, and give new examples including almost Kaehler manifolds and Schwarzshild black holes with a $b$-field., Comment: 35 pages, LaTeX, Comments and references added, a part of Sec. 5.1 deleted, published version

We argue that MQCD admits intersecting domain walls that are realized as Cayley calibrations of the MQCD M5-brane. We discuss various dual realizations and comment on how branes can realise domain walls in N=1 supersymmetric theories in D=3., Comment: 10 pages. Very minor changes. Version to be published in Phys. Lett. B

We find the combinations of momentum and domain-wall charges corresponding to BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how the supersymmetry algebra implies their stability. These states form the boundary of the convex cone associated with the Jordan algebra of $4\times 4$ real symmetric matrices, and we explore some implications of the associated geometry. For the Wess-Zumino model we derive the conditions for preservation of 1/4 supersymmetry when one of two parallel domain-walls is rotated and in addition show that this model does not admit any classical configurations with 3/4 supersymmetry. Our analysis also provides information about BPS states of N=1 D=4 anti-de Sitter supersymmetry., Comment: Latex, 27 pages. Various corrections and improvements including an expanded discussion on BPS states in adS

We show how non-near horizon p-brane theories can be obtained from two embedding constraints in a flat higher dimensional space with 2 time directions. In particular this includes the construction of D3 branes from a flat 12-dimensional action, and M2 and M5 branes from 13 dimensions. The worldvolume actions are determined by constant forms in the higher dimension, reduced to the usual expressions by Lagrange multipliers. The formulation affords insight in the global aspects of the spacetime geometries and makes contact with recent work on two-time physics., Comment: 29 pages, 10 figures, Latex using epsf.sty and here.sty; v2: reference added and some small corrections

We study the stabilization of scalars near a supersymmetric black hole horizon using the equation of motion of a particle moving in a potential and background metric. When the relevant 4-dimensional theory is described by special geometry, the generic properties of the critical points of this potential can be studied. We find that the extremal value of the central charge provides the minimal value of the BPS mass and of the potential under the condition that the moduli space metric is positive at the critical point. We relate these ideas to the Weinhold and Ruppeiner metrics introduced in the geometric approach to thermodynamics and used for study of critical phenomena., Comment: 19 pages, Latex

Geometric Killing spinors which exist on AdS_{p+2} X S^{d-p-2} sometimes may be identified with supersymmetric Killing spinors. This explains the enhancement of unbroken supersymmetry near the p-brane horizon in d dimensions. The corresponding p-brane interpolates between two maximally supersymmetric vacua, at infinity and at the horizon. New case is studied here: p=0, d=5. The details of supersymmetric version of the very special geometry are presented. We find the area-entropy formula of the supersymmetric 5d black holes via the volume of S^3 which depends on charges and intersection matrix., Comment: 13 pages, Latex

Instanton and seven-brane solutions of type IIB supergravity carrying charges in the Ramond-Ramond sector are constructed. The singular seven-brane has a quantized \RR \ \lq magnetic' charge whereas its dual is the instanton, which is non-singular in the string frame and has an associated {\it global} \lq electric' charge. The product of these charges is constrained by a Dirac quantization condition. The instanton has the form of a space-time wormhole in the string frame, and is responsible for the non-conservation of the Noether current., Comment: PHYZZX macros. 13 pages. Final version as it will appear in Phys. Lett. B (typos corrected)

We examine the two-dimensional spacetimes that emerge from string theory. We find all the solutions with no tachyons, and show that the only non-trivial solution is the black hole spacetime. We examine the role of duality in this picture. We then explore the thermodynamics of these solutions which is complicated by the fact that only in two spacetime dimensions is it impossible to redefine the dilaton field in terms of a canonical scalar field. Finally, we extend our analysis to the heterotic string, and briefly comment on exact, as opposed to perturbative, solutions.