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Along the lines of the Einstein-Rosen wave equation of General Relativity (GR), we derive a gravitational wave equation with cylindrical symmetry in the Einstein-aether (EA) theory. We show that the gravitational wave in the EA is periodic in time for both the metric functions $\Psi(r,t)$ and $H(r,t)$. However, in GR, $\Psi(r,t)$ is periodic in time, but $H(r,t)$ is semi-periodic in time, having a secular drifting in the wave frequency. The evolution of wave pulses of a given width is entirely different in both theories in the $H(r,t)$ metric function due to this frequency drifting. Another fundamental difference between the two theories is the gravitational wave velocity. While in GR, the waves propagate with the speed of light, in EA, there is no upper limit to the wave velocity, reaching infinity if $c_{13} \rightarrow 1$ and zero if $c_{13} \rightarrow -\infty$. We also show that energy-momentum pseudotensor and superpotential get contributions from aether in addition to the usual gravitational field part. All these characteristics are observational signatures that differentiate GR and EA., Comment: 26 pages, 10 figures. We have corrected the initial conditions for $H(r,t)$ in order to have $\Psi(r,t)$ not equal to $H(r,t)$

We attempt to answer whether Birkhoff's theorem (BT) is valid in the Einstein-Aether (EA) theory. The BT states that any spherically symmetric solution of the vacuum field equations must be static, unique, and asymptotically flat. For a general spherically symmetric metric with metric functions $A(r,t)$ \& $B(r,t)$, and aether components $a(r,t)$ \& $b(r,t)$, we prove the conditions for the staticity of spacetime using two different methods. We point out that BT is valid in EA theory only for special values of $c_1+c_3$, $c_1+c_4$, and $c_2$, where we can show that all these special cases are asymptotically flat. In particular, when the aether has only a temporal component, i.e., $b(r,t)=0$ and the $c_{14} \neq 0$ case gives us spherically symmetric static black holes without horizons; that is, they have naked singularities, at least for special values of $c_{14}$. Thus, the cosmic censorship conjecture is violated for the case BT holds. However, when we have an aether vector with temporal and radial components, we only prove that the staticity and the flatness at infinity hold for a special metric and particular combination of the aether parameters. For this case, there exist universal horizons instead of naked singularities., Comment: 19 pages, no figures

We analyze several spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether (EA) theory with a non static aether and study the thermodynamics of their Killing and universal horizons. We show that there are five classes of solutions corresponding to different values of a combination of the free parameters, $c_{2}$, $c_{13}=c_1+c_3$ and $c_{14}=c_1+c_4$, which are: (A) $c_2 \ne 0$ and $c_{13} \ne 0$ and $c_{14}=0$, (B) $c_2 \ne 0$ and $c_{13} = 0$ and $c_{14} = 0$, (C) $c_2 = 0$ and $c_{13} \ne 0$ and $c_{14} = 0$, (D) $c_2 = 0$, $c_{13} = 0$ and $c_{14} \ne 0$, and (E) $c_2 = - c_{13} \ne 0$ and $c_{14} \ne 0$. We present explicit analytical solutions for these five cases. All these cases have singularities at $r=0$ and are asymptotically flat spacetimes and possess both Killing and universal horizons with the universal horizons always being inside the Killing horizons. Finally, we compute the surface gravity, the temperature, the entropy and the first law of thermodynamics for the universal horizons., Comment: 35 pages, 5 figures and 4 tables. We have improved the manuscript with a new solution and a comparison with others authors who have used Eddington-Finkelstein coordinates

The Vector-Tensor (VT) theories of gravity are a class of alternative theories to General Relativity (GR) that are characterized by the presence of a dynamical vector field besides the metric. They are studied in attempts to understand spontaneous Lorentz violation, to generate massive gravitons, and as models of dark matter and dark energy. In this article, I outline how the nature of singularities and horizons in VT theories differ greatly from GR even under the same ordinary conditions. This is illustrated with Einsteinaether theory where vacuum black hole solutions have naked singularities and vacuum cosmological solutions have new singularities that are otherwise absent in GR. It would be interesting to explore these deviations using gravitational waves, Comment: 9 pages, Invited parallel session talk at MG16, to appear in the Proceedings of the Sixteenth Marcel Grossmann Meeting

In the present work we analyze all the possible spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether theory with static aether. We show that there are four classes of solutions corresponding to different values of a combination of the free parameters, $c_{14}=c_1+c_4$, which are: $ 0 < c_{14}<2$, $c_{14} < 0$, $c_{14}=2$ and $c_{14}=0$. We present explicit analytical solutions for $c_{14}=3/2, 16/9, 48/25, -16, 2$ and $0$. The first case has some pathological behavior, while the rest have all singularities at $r=0$ and are asymptotically flat spacetimes. For the solutions $c_{14}=16/9, 48/25\, \mathrm{\, and \,}\, -16$ we show that there exist no horizons, neither Killing nor universal horizon, thus we have naked singularities. Finally, the solution for $c_{14}=2$ has a metric component as an arbitrary function of radial coordinate, when it is chosen to be the same as in the Schwarzschild case, we have a physical singularity at finite radius, besides the one at $r=0$. This characteristic is completely different from General Relativity., Comment: 21 pages and 9 figures

How do the global properties of a Lorentzian manifold change when endowed with a vector field? This interesting question is tackled in this paper within the framework of Einstein-Aether (EA) theory which has the most general diffeomorphism-invariant action involving a spacetime metric and a vector field. After classifying all the possible nine vacuum solutions with and without cosmological constant in Friedmann-Lema{\^{\i}}tre-Robertson-Walker (FLRW) cosmology, we show that there exist three singular solutions in the EA theory which are not singular in the General Relativity (GR), all of them for $k=-1$, and another singular solution for $k=1$ in EA theory which does not exist in GR. This result is cross-verified by showing the focusing of timelike geodesics using the Raychaudhuri equation. These new singular solutions show that GR and EA theories can be completely different, even for the FLRW solutions when we go beyond flat geometry ($k=0$). In fact, they have different global structures. In the case where $\Lambda=0$ ($k=\pm 1$) the vector field defining the preferred direction is the unique source of the curvature., Comment: 9 pages and no figures. Some typos are corrected in this version and included an additional discussion in the Conclusions. Accepted for publication in JCAP

The Einstein-Aether (EA) theory belongs to a class of modified gravity theories characterized by the introduction of a time-like unit vector field, called aether. In this scenario, a preferred frame arises as a natural consequence of a broken Lorentz invariance. In the present work we have obtained and analyzed some exact solutions allowed by this theory for two particular cases of perfect fluid, both with Friedmann-Lemaitre-Robertson-Walker (FLRW) symmetry: (i) a fluid with constant energy density ($p=-\rho_0$), and (ii) a fluid with zero energy density ($\rho_0=0$), corresponding to the vacuum solution with and without cosmological constant ($\Lambda$), respectively. Our solutions show that the EA and GR theories do not differentiate each other only by the coupling constants. This difference is clearly shown because of the existence of singularities that there are not in GR theory. This characteristic appears in the solutions with $p=-\rho_0$ as well as with $\rho_0=0$, where this last one depends only on the aether field. Besides, we consider the term of the EA theory in the Raychaudhuri equation and discuss the meaning of the strong energy condition in this scenario and found that this depends on aether field. The solutions admit an expanding or contracting system. A bounce, a singular, a constant and an accelerated expansion solutions were also obtained, exhibiting the richness of the EA theory from the dynamic point of view of a collapsing system or of a cosmological model. The analysis of energy conditions, considering an effective fluid shows that the term of the aether contributes significantly for the accelerated expansion of the system for the case in which the energy density is constant. On the other hand, for the vacuum case ($\rho_0=0$), the energy conditions are all satisfied for the aether fluid., Comment: 21 pages, 5 figures. Accepted for publication in Canadian Journal of Physics

Studying particle motion in the gravitational field of a black hole from the perspective of different observers is important for separating the coordinate artifacts from the physical phenomena. In this paper, we show that a freely falling test particle exhibits gravitational repulsion by a black hole as seen by an asymptotic observer, whereas nothing of the kind happens as recorded by a freely falling observer or by an observer located at a finite distance from the event horizon. This analysis is carried out for a general Reissner-Nordstr\"om, an extremal Reissner-Nordstr\"om, and a Schwarzschild black hole. We are lead to conclude that the origin of these bizarre results lies in the fact that the quantities measured by the different observers are neither Lorentz scalars nor gauge invariant., Comment: 10 pages, 6 figures

The dynamics of a radiating charge is one of the oldest unsettled problems in classical physics. The standard Lorentz-Abraham-Dirac (LAD) equation of motion is known to suffer from several pathologies and ambiguities. This paper briefly reviews these issues, and reports on a new model that fixes these difficulties in a natural way. This model is based on a hypothesis that there is an infinitesimal time delay between action and reaction. This can be related to Feynman's regularization scheme, leading to a quasi-local QED with a natural UV cutoff, hence without the need for renormalization as the divergences are absent. Besides leading to a pathology-free equation of motion, the new model predicts a modification of the Larmor formula that is testable with current and near future ultra-intense lasers., Comment: 6 pages. The title and Eq. 4 were slightly modified in this version. To appear in the Proceedings of Group-31 (The 31st International Colloquium on Group Theoretical Methods in Physics)

General Relativity has had tremendous successes on both theoretical and experimental fronts for over a century by now. However, the theory contents are far from being exhausted. Only very recently, with gravitational wave detection from colliding black holes, have we started probing gravity behavior in the strongly non-linear regime. Even today, black hole studies keep revealing more and more paradoxes and bizarre results. In this paper, inspired by David Hilbert's startling observation, we show that, contrary to the conventional wisdom, a freely falling test particle feels gravitational repulsion by a black hole as seen by an asymptotic observer. We dig deeper into this relativistic gravity surprising behavior and offer some explanations., Comment: 4 pages, title is changed and the text is significantly modified

In this paper, we show the existence of static and rotating universal horizons and black holes in gravitational theories with the broken Lorentz invariance. We pay particular attention on the ultraviolet regime, and show that universal horizons and black holes exist not only in low energy scales but also in the UV scales. This is realized by presenting various static and stationary exact solutions of the full theory of the projectable Ho\v{r}ava gravity with an extra U(1) symmetry in (2+1)-dimensions, which, by construction, is power-counting renormalizable., Comment: revtex4, no tables, 21 figures. Typos were corrected. Phys. Rev. D93 (2016) 124025

Non-stationary null dust in a spherically symmetric spacetime is studied in the context of a general-covariant Horava-Lifshitz theory. The non-minimal coupling to matter is considered in the infrared limit. The aim of this paper is to study whether the collapse of a null dust-like fluid can be a solution of Ho\v{r}ava-Lifshitz theory in the infrared limit. We have shown that the unique possible solution is static. This solution represents a Minkowski spacetime since the energy density is null., Comment: 6 pages. Corrected some typos and added new references. To appear in Canadian Journal of Physics

The quantization of two-dimensional Ho\v{r}ava theory of gravity without the projectability condition is considered. Our study of the Hamiltonian structure of the theory shows that there are two first-class and two second-class constraints. Then, following Dirac we quantize the theory by first requiring that the two second-class constraints be strongly equal to zero. This is carried out by replacing the Poisson bracket by the Dirac bracket. The two first-class constraints give rise to the Wheeler-DeWitt equations, which yield uniquely a plane-wave solution for the wavefunction. We also study the classical solutions of the theory and find that the characteristics of classical spacetimes are encoded solely in the phase of the plane-wave solution in terms of the extrinsic curvature of the foliations $t =$Constant, where $t$ denotes the globally-defined time of the theory., Comment: revtex4, no figures & tables. A program and New references are added. Version to appear in PRD

Since Stephen Hawking discovered that black holes emit thermal radiation, black holes have become the theoretical laboratories for testing our ideas on quantum gravity. This dissertation is devoted to the study of singularities, the formation of black holes by gravitational collapse and the global structure of spacetime. All our investigations are in the context of a recently proposed approach to quantum gravity, which breaks Lorentz and diffeomorphism symmetries at very high energies., Comment: XIV+147 pages, 19 figures, PhD Thesis, Baylor University

Given that the scale of quantum gravity is not experimentally accessible, one naturally resorts to mathematical consistency as a measure for a good candidate theory to replace General Relativity at high energies. Reproducing the semi-classical results of black hole entropy has become a standard test for any prospective theory of quantum gravity. It is often argued that another such commonality, albeit less known, is the similar fractal behaviour. It is shown that many, if not all, approaches to quantum gravity predict a spectral dimension of 2 in ultraviolet regime. In this paper, by computing the heat kernel, we show that the spectral dimension of closed bosonic string theory is 26. We discuss the implications of this disparity., Comment: 4 pages, new reference added, published version

General Relativity is known to break down at singularities. However, it is expected that quantum corrections become important when the curvature is of the order of Planck scale avoiding the singularity. By calculating the effect of tidal forces on a freely falling inertial frame, and assuming the least possible size of the frame to be of the Planck length, we show that the Lorentz frames cease to exist at a finite distance from the singularity. Within that characteristic radius, one cannot apply General Relativity nor Quantum Field Theory as we know them today. Additionally we consider other quantum length scales and impose limits on the distances from the singularity at which those theories can conceivably be applied within a Lorentz frame., Comment: 7 pages. This essay received an honorable mention in the Gravity Research Foundation 2013 Awards for Essays on Gravitation

We study gravitational collapse of a spherical fluid in nonrelativistic general covariant theory of the Ho\v{r}ava-Lifshitz gravity with the projectability condition and an arbitrary coupling constant $\lambda$, where $|\lambda - 1|$ characterizes the deviation of the theory from general relativity in the infrared limit. The junction conditions across the surface of a collapsing star are derived under the (minimal) assumption that the junctions be mathematically meaningful in terms of distribution theory. When the collapsing star is made of a homogeneous and isotropic perfect fluid, and the external region is described by a stationary spacetime, the problem reduces to the matching of six independent conditions. If the perfect fluid is pressureless (a dust fluid), it is found that the matching is also possible. In particular, in the case $\lambda = 1$, the external spacetime is described by the Schwarzschild (anti-) de Sitter solution written in Painlev\'e-Gullstrand coordinates. In the case $\lambda \not= 1$, the external spacetime is static but not asymptotically flat. Our treatment can be easily generalized to other versions of Ho\v{r}ava-Lifshitz gravity or, more generally, to any theory of higher-order derivative gravity., Comment: revtex4, 4 figures. Phys. Rev. D88, 024044 (2013)

We systematically study black holes in the Horava-Lifshitz (HL) theory by following the kinematic approach, in which a horizon is defined as the surface at which massless test particles are infinitely redshifted. Because of the nonrelativistic dispersion relations, the speed of light is unlimited, and test particles do not follow geodesics. As a result, there are significant differences in causal structures and black holes between general relativity (GR) and the HL theory. In particular, the horizon radii generically depend on the energies of test particles. Applying them to the spherical static vacuum solutions found recently in the nonrelativistic general covariant theory of gravity, we find that, for test particles with sufficiently high energy, the radius of the horizon can be made as small as desired, although the singularities can be seen in principle only by observers with infinitely high energy. In these studies, we pay particular attention to the global structure of the solutions, and find that, because of the foliation-preserving-diffeomorphism symmetry, ${Diff}(M,{\cal{F}})$, they are quite different from the corresponding ones given in GR, even though the solutions are the same. In particular, the ${Diff}(M,{\cal{F}})$ does not allow Penrose diagrams. Among the vacuum solutions, some give rise to the structure of the Einstein-Rosen bridge, in which two asymptotically flat regions are connected by a throat with a finite non-zero radius. We also study slowly rotating solutions in such a setup, and obtain all the solutions characterized by an arbitrary function $A_{0}(r)$. The case $A_{0} = 0$ reduces to the slowly rotating Kerr solution obtained in GR., Comment: latex4, 15 figures. Some typos were corrected

We study spherically symmetric static spacetimes generally filled with an anisotropic fluid in the nonrelativistic general covariant theory of gravity. In particular, we find that the vacuum solutions are not unique, and can be expressed in terms of the $U(1)$ gauge field $A$. When solar system tests are considered, severe constraints on $A$ are obtained, which seemingly pick up the Schwarzschild solution uniquely. In contrast to other versions of the Horava-Lifshitz theory, non-singular static stars made of a perfect fluid without heat flow can be constructed, due to the coupling of the fluid with the gauge field. These include the solutions with a constant pressure. We also study the general junction conditions across the surface of a star. In general, the conditions allow the existence of a thin matter shell on the surface. When applying these conditions to the perfect fluid solutions with the vacuum ones as describing their external spacetimes, we find explicitly the matching conditions in terms of the parameters appearing in the solutions. Such matching is possible even without the presence of a thin matter shell., Comment: Singular behavior of the fluid at the center is clarified. New references are added. Version to appear in JCAP

The constraint on the ADD model of extra dimensions coming from photon annihilation into Kaluza-Klein graviton in supernova cores is revisited. In the two photon process for a conservative choice of the core parameters, we obtain the bound on the fundamental Planck scale $M_* \gtrsim$ 1.6 TeV. The combined energy loss rate due to nucleon-nucleon brehmstrahlung and photon annihilation processes is rederived, which shows that the combined bounds add only second decimal place to $M_*$. The present study can strengthen the results that are available in the current literature for the graviton emission from SN1987A which puts a very strong constraints on models with large extra dimensions for the case of $n=3$ ., Comment: To appear in JCAP

In large extra dimensional Kaluza-Klein (KK) scenario, where the usual Standard Model (SM) matter is confined to a 3+1-dimensional hypersurface called the 3-brane and gravity can propagate to the bulk (D=4+d, d being the number of extra spatial dimensions), the light graviton KK modes can be produced inside the supernova core due to the usual nucleon-nucleon bremstrahlung, electron-positron and photon-photon annihilations. This photon inside the supernova becomes plasmon due to the plasma effect. In this paper, we study the energy-loss rate of SN 1987A due to the KK gravitons produced from the plasmon-plasmon annihilation. We find that the SN 1987A cooling rate leads to the conservative bound $M\_D$ > 22.9 TeV and 1.38 TeV for the case of two and three space-like extra dimensions., Comment: 13 pages, 1 ps figure, text is modified a little bit, conclusion unchanged, new references are added, version accepted for publication in PRD

Gravity is one of the most inexplicable forces of nature, controlling everything, from the expansion of the Universe to the ebb and flow of ocean tides. The search for the laws of motion and gravitation began more than two thousand years ago but still we do not have the complete picture of it. In this article, we have outlined how our understanding of gravity is changing drastically with time and how the previous explanations have shaped the most recent developments in the field like superstrings and braneworlds., Comment: 21 pages