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Ketamine is a noncompetitive antagonist at the glutamatergic N-methyl-D-aspartate (NMDA) receptor that is used in human and animal medicine as an injectable anesthetic. The illegal use of ketamine as a recreational drug is rapidly growing. Very little is currently known about the consequences of repeated ketamine exposure in the human brain. Animal studies indicate that the prefrontal dopaminergic system is particularly vulnerable to the toxic effects of repeated administration of NMDA antagonists. In this study, dopamine D1 receptor availability was assessed by using positron emission tomography and the selective D1 receptor radioligand [11C]NNC 112 in a group of 14 recreational chronic ketamine users and matched healthy subjects.History of ketamine abuse was confirmed in subjects by hair analysis. [11C]NNC 112 binding potential was measured with kinetic analysis using the arterial input function.Dorsolateral prefrontal cortex D1 receptor availability was significantly up-regulated in chronic ketamine users ([11C]NNC 112 binding potential: mean=1.68 ml/g, SD=0.40) relative to comparison subjects (mean=1.35 ml/g, SD=0.35). No significant differences were noted in other cortical, limbic, or striatal regions. In the chronic ketamine user group, dorsolateral prefrontal cortex [11C]NNC 112 binding potential up-regulation was significantly correlated with the number of vials of ketamine (with a vial representing approximately 200-300 mg of ketamine) used per week.Chronic ketamine users exhibited a regionally selective up-regulation of D1 receptor availability in the dorsolateral prefrontal cortex, a phenomenon observed following chronic dopamine depletion in animal studies. These data suggest that the repeated use of ketamine for recreational purposes affects prefrontal dopaminergic transmission, a system critically involved in working memory and executive function.

(-)-N-(11)C-propyl-norapomorphine ((11)C-NPA) is a new dopamine agonist PET radiotracer that holds potential for imaging the high-affinity states of dopamine D(2)-like receptors in the living brain. The goal of this study was to develop and evaluate analytic strategies to derive in vivo (11)C-NPA binding parameters.Two baboons were scanned 4 times after (11)C-NPA injections. The metabolite-corrected arterial input functions were measured. Regional brain time-activity curves were analyzed with kinetic and graphical analyses, using the arterial time-activity curve as the input function. Data were also analyzed with the simplified reference-tissue model (SRTM) and graphical analysis with reference-region input.(11)C-NPA exhibited moderately fast metabolism, with 31% +/- 5% of arterial plasma concentration corresponding to the parent compound at 40 min after injection. Plasma clearance was 29 +/- 1 L/h, and plasma free fraction (f(1)) was 5% +/- 1%. For kinetic analysis, a 1-tissue compartment model (1TCM) provided a good fit to the data and more robust derivations of the tissue distribution volumes (V(T), in mL/g) than a 2-tissue compartment model (2TCM). Using 1TCM, V(T)s in the cerebellum and striatum were 3.4 +/- 0.4 and 7.5 +/- 2 mL/g, respectively, which led to estimates of striatal binding potential (BP) of 4.0 +/- 1.1 mL/g and striatal equilibrium specific-to-nonspecific partition coefficient (V(3)") of 1.2 +/- 0.2. V(T) values derived with graphical analysis were well correlated with but slightly lower than V(T) values derived with kinetic analysis. V(3)" values derived with SRTM were well correlated with but slightly higher than V(3)" values derived with kinetic analysis. Using any method, a significant difference was detected in BP and V(3)" values between the 2 animals. It was determined that 30 min of scanning data were sufficient to derive V(3)" values using kinetic, graphical (arterial input and reference-region input), and SRTM analyses.This study indicates that (11)C-NPA is a suitable PET tracer to quantify the agonist high-affinity sites of D(2)-like receptors.

The fundamental pathological process(es) associated with schizophrenia remain(s) uncertain, but multiple lines of evidence suggest that this condition is associated with (1) excessive stimulation of striatal dopamine (DA) D2 receptors, (2) deficient stimulation of prefrontal DA D1 receptors and, (3) alterations in prefrontal connectivity involving glutamate (GLU) transmission at N-methyl-d-aspartate (NMDA) receptors. This chapter first briefly discusses the current knowledge status for these abnormalities, with emphasis on results derived from clinical molecular imaging studies. The evidence for hyperstimulation of striatal D2 receptors rests on strong pharmacological evidence and has recently received support from brain imaging studies. The hypothesis of deficient prefrontal cortex (PFC) D1 receptor stimulation is almost entirely derived from preclinical studies. Preliminary imaging data compatible with this hypothesis have recently emerged. The NMDA hypofunction hypothesis originates mainly from indirect pharmacological data. The interactions between DA and GLU systems relevant to schizophrenia are then reviewed. Animal and imaging data supporting the general model that the putative DA imbalance in schizophrenia (striatal excess and cortical deficiency) might be secondary to NMDA hypofunction in the PFC and its connections are presented. Equally important are the potential consequences of this DA imbalance for NMDA function in the striatum and the cortex, which are subsequently discussed. In conclusion, it is proposed that schizophrenia is associated with strongly interconnected abnormalities of GLU and DA transmission: NMDA hypofunction in the PFC and its connections might generate a pattern of dysregulation of DA systems that, in turn, further weakens NMDA-mediated connectivity and plasticity.

A positive experience during a first encounter with a drug of abuse is predictive of subsequent use and might represent a vulnerability factor to develop addiction. This paper presents a meta-analysis of data acquired in 60 healthy volunteers who underwent a low-dose amphetamine challenge (0.3 mg/kg, i.v.) during imaging of dopamine D2 receptor availability with SPECT and the D2/D3 radiotracer [123I]IBZM. Amphetamine-stimulated DA release induced a small, significant and highly variable decrease in striatal D2 receptor availability (-8.3 +/- 6.7%). The magnitude of the decrease in D2 receptor availability was significantly associated with the positive reinforcing effects of the drug reported by the subject (r2 = 0.14, p = 0.003). Age was associated with decreased potency of dopamine to elicit positive reinforcing effects. This study indicates that both a large dopaminergic response and young age during a first encounter with a drug of abuse potential contribute to higher positive reinforcing effects.

Background Lower serotonergic activity correlates with high-lethality suicide attempts in major depression. Postmortem studies of serotonin receptors in suicides localize changes to the ventral prefrontal cortex (PFC). We studied serotonergic response in ventral PFC in depressed patients surviving a high-lethality suicide attempt. Methods Depressed patients with a history of a high-lethality suicide attempt(n = 16) were compared with those with low-lethality attempts (n = 9) for level of depression, suicidal intent and ideation, impulsivity, aggression, and neuropsychological test performance. Subjects were scanned while medication free after a single-blind placebo and after fenfluramine hydrochloride administration on a second day. Brain responses were measured by positron emission tomography imaging of fludeoxyglucose F 18 and serial prolactin levels. Scans were compared by means of statistical parametric mapping. Correlations of changes in relative regional cerebral uptake (rCMRglu) with clinical and neuropsychological measures were assessed. Results Depressed high-lethality suicide attempters had lower rCMRglu in ventral, medial, and lateral PFC compared with low-lethality attempters. This difference was more pronounced after fenfluramine administration. Lower ventromedial PFC activity was associated with lower lifetime impulsivity, higher suicidal intent (planning), and higher-lethality suicide attempts. Higher verbal fluency was positively correlated with rCMRglu in the same regions. Conclusions Prefrontal localized hypofunction and impaired serotonergic responsivity are proportional to the lethality of the suicide attempt and may mediate the effects of suicide intent and impulsivity on lethality. Positron emission tomographic neuroreceptor studies are needed to determine whether postmortem serotonin receptor findings are also present in vivo and contribute to the abnormal rCMRglu responses.

A new PET radioligand for the serotonin transporter (SERT), [11C]-5-bromo-2-[2-(dimethylaminomethylphenylsulfanyl)]phenylamine ([11C]DAPA (10), was synthesized and evaluated in vivo in rats and baboons. [11C]DAPA (10) was prepared from its monomethylamino precursor 8 by reaction with high specific activity [11C]methyl iodide. Radiochemical yield was 24 +/- 5% based on [11C]methyl iodide at end of bombardment (EOB, n = 10) and specific activity was 1,553 +/- 939 Ci/mmol at end of synthesis (EOS, n = 10). Binding assays indicated that [11C]DAPA displays high affinity (Ki 1.49 +/- 0.28 nM for hSERT) and good selectivity for the SERT in vitro. Biodistribution studies in rats indicated that [11C]DAPA enters into the brain readily and localizes in brain regions known to contain high concentrations of SERT, such as the thalamus, hypothalamus, frontal cortex and striatum. Moreover, such binding in SERT-rich regions of the brain are blocked by pretreatment with either the selective serotonin reuptake inhibitor (SSRI) citalopram and by the cold compound itself, demonstrating that [11C]DAPA binding in the rat brain is saturable and specific to SERT. Imaging experiments in baboons indicated that [11C]DAPA binding is consistent with the known distribution of SERT in the baboon brain, with highest levels of radioactivity detected in the midbrain and thalamus, intermediate levels in the hippocampus and striatum, and lower levels in the cortical regions. Pretreatment of the baboon with citalopram 10 min before radioactivity injection blocked the binding of [11C]DAPA in all brain regions that contain SERT. Kinetic analysis revealed that, in all brain regions examined, [11C]DAPA specific to nonspecific distribution volume ratios (V(3)") are higher than [11C](+)-McN 5652 and similar to [11C]DASB. In summary, [11C]DAPA appears to be a promising radioligand suitable for the visualization of SERT in vivo using PET.

Our goal was to synthesize with high specific activity R(-)-1-(2,5-Dimethoxy-4-[ 123 I]iodophenyl)-2-aminopropane [R(-)[ 123 I]DOI], an in vitro potent and selective 5-HT 2A/2C serotonin agonist, and study in vivo its plasma pharmacokinetics and brain distribution in baboon by SPECT. The purpose was to evaluate this radiotracer as a potential tool in discerning the role of the agonist high affinity state of 5-HT 2 receptors in depression and other neurological disorders. The radiotracer was prepared by electrophilic radioiodination of the N-trifluoroacetyl precursor of R(-)-1-(2,5-Dimethoxyphenyl)-2-aminopropane [R(-)DMA-TFA] with high-purity sodium [ 123 I]iodide in the presence of chloramine-T, followed by amino deprotection with KOH in isopropanol (labeling yield: 73%, radiochemical yield: 62%, radiochemical purity: 99%). In vivo studies in baboon showed high accumulation of radioactivity in thalamus, the frontoparietal cortex, temporal, occipital and the striatum regions, with slightly lower accumulation in the midbrain and cerebellum. Ketanserin did not displaced the radioactivity in any of these brain regions. Plasma metabolite analysis was performed using methanol protein precipitation, the methanol fractions contained from 68% to 92% of the mixture of a labeled metabolite and parent compound. The recovery coefficient of unmetabolized R(-)[ 123 I]DOI was 68%. The percent parent compound present in the extracted fraction, measured by HPLC, decreased gradually with time from 99.8% to 0.3% still present after 4.7 hours post injection whereas the percentage of the only one detected metabolite increased conversely. Free fraction determination (f 1 ), was 31 ± 0.9% (n = 3). For comparison purposes, ex-vivo brain distribution, displacement and metabolite analysis was also carried out in rodents. Although R(-)[ 123 I]DOI displayed good brain uptake and localized in serotonergic areas of the brain, its target to non target ratio and its insensitivity to ketanserin displacement suggest high nonspecific uptake, therefore non potentially useful as brain imaging radiotracer for visualization of the agonist high-affinity state of 5-HT 2A receptors and for visualizing 5-HT 2C receptors by SPECT.

The classical dopamine hypothesis of schizophrenia proposes that positive symptoms of the disorder are a result of hyperactivity of dopamine transmission.1 This hypothesis has received new support from brain imaging studies that have shown an exaggerated response to acute amphetamine challenge in untreated patients with schizophrenia compared with healthy subjects using dopamine D2 receptor SPECT (single photon emission computed tomography) or PET (positron emission tomography).2–4

D. Martinez1 °, M. Slifstein1, N. Nabulsi2, A. Grassetti1, N. Urban1, A. Perez1, F. Liu1, S. Lin2, J. Ropchan2, X. Mao3, L.S. Kegeles1, D. Shungu3, R.E. Carson4, Y. Huang2 1Columbia University, Department of Psychiatry, New York, USA; 2Yale University, Yale PET Center, New Haven, USA; 3Weill Medical College of Cornell University, Department of Radiology, New York, USA; 4Yale University, Yale PET Center, New York, USA

A 40 base polymorphism of a variable number of tandem repeats (VNTR) has been described in the 3' untranslated region of the gene (SLC6A3) coding for the dopamine transporter (DAT). Despite being located in the untranslated region of the gene, this polymorphism has been associated with clinical phenotypes associated with dysregulation of dopamine transmission, such as attention deficit hyperactivity disorder and cocaine-induced paranoia. To examine the neurochemical phenotype associated with this polymorphism, we compared amphetamine-induced dopamine release (measured as displacement of the radiotracer [123I]IBZM) and DAT expression (measured with [123I]beta-CIT) in the striatum with Single Photon Computerized Emission Tomography (SPECT). Our sample included 59 subjects, 31 healthy controls and 29 patients with schizophrenia. No significant association was found between VNTR polymorphism and amphetamine-induced dopamine release or DAT density in the total sample, nor when each diagnostic group was considered separately. Thus, we did not replicate the findings of two previous studies, which had suggested that the 9 repeat allele was associated with either an increased or decreased DAT expression, albeit in different patient populations.

OBJECTIVE: The antidepressant action of ECT may be related to its anticonvulsant properties. Positron emission tomography (PET) studies of regional cerebral metabolic rate for glucose were used to test this hypothesis. METHOD: Ten patients with major depression were studied with PET before and approximately 5 days after a course of bilateral ECT. Statistical parametric mapping was used to identify regions of decreased cerebral glucose metabolism. RESULTS: Widespread regions of decreased regional cerebral glucose metabolism were identified after ECT, especially in the frontal and parietal cortex, anterior and posterior cingulate gyrus, and left temporal cortex. A region-of-interest analysis similarly indicated post-ECT reductions in regional cerebral glucose metabolism. CONCLUSIONS: ECT reduces neuronal activity in selected cortical regions, a potential anticonvulsant and antidepressant effect.

The classical dopamine hypothesis of schizophrenia postulates a hyperactivity of dopaminergic transmission at the D 2 receptor. We measured in vivo occupancy of striatal D 2 receptors by dopamine in 18 untreated patients with schizophrenia and 18 matched controls, by comparing D 2 receptor availability before and during pharmacologically induced acute dopamine depletion. Acute depletion of intrasynaptic dopamine resulted in a larger increase in D 2 receptor availability in patients with schizophrenia (19% ± 11%) compared with control subjects (9% ± 7%, P = 0.003). The increased occupancy of D 2 receptors by dopamine occurred both in first-episode neuroleptic-naive patients and in previously treated chronic patients experiencing an episode of illness exacerbation. In addition, elevated synaptic dopamine was predictive of good treatment response of positive symptoms to antipsychotic drugs. This finding provides direct evidence of increased stimulation of D 2 receptors by dopamine in schizophrenia, consistent with increased phasic activity of dopaminergic neurons.

The hippocampus is a site of previously reported structural and functional abnormalities in schizophrenia. We used magnetic resonance imaging (MRI) and proton magnetic resonance spectroscopy (MRS) to measure gray matter volumes, the neuronal marker N-acetylaspartate (NAA), and the combination of glutamate (Glu), glutamine (Gln), and gamma-aminobutyric acid (GABA), designated Glx. Measurements were obtained of the medial temporal lobe, centered on the hippocampus, in 10 male patients with schizophrenia (3 neuroleptic-medicated and 7 medication-free), and 10 matched normal volunteers. MRI volumetric measurements and MRS data obtained with short echo time (TE=20 ms) one-dimensional STEAM chemical shift imaging (CSI) on a GE 1.5 Tesla Signa system were analyzed. A laterality index ?(L-R)/(L+R) was generated from the ratio of Glx to choline-containing compounds (Cho) to test asymmetry changes. Reliability of the MRS measures was assessed with five test-retest studies of healthy volunteers and showed coefficients of variation (CV) in the range of 36-44% for the MRS ratios and standard deviations (S.D.) of 0.15-0.17 for the laterality indices. The Glx/Cho laterality index showed a relative right-sided excess in this region in the patients (-0.23+/-0.20) compared to the controls (+0.06+/-0.20), which was not confounded by tissue composition or placement variability of the MRS voxels. Hippocampal volume deficit and asymmetry were not significant, and other MRS measures showed no differences between patients and controls. The preliminary finding of a lateralized abnormality in Glx is consistent with postmortem findings of asymmetric neurochemical temporal lobe abnormalities in schizophrenia.

Background: Abnormalities of dopamine function in schizophrenia are suggested by the common antidopaminergic properties of antipsychotic medications. However, direct evidence of a hyperdopaminergic state in schizophrenia has been difficult to demonstrate, given the difficulty to measure dopamine transmission in the living human brain. Such evidence has recently emerged. Three studies reported an increase in dopamine transmission following acute amphetamine challenge in patients with schizophrenia compared to matched healthy control subjects, thus demonstrating a dysregulation of dopamine in schizophrenia. In all studies, a large variance was observed within the schizophrenic group in the magnitude of this finding, and clinical predictors of this effect could not be identified. Methods: In this paper, we combined previously published and newly acquired data to obtain sufficient power to address this question. Results: The most important findings derived from this extended data set are: 1) dysregulation of dopamine function revealed by the amphetamine challenge is present at onset of illness and in patients never previously exposed to neuroleptic medications; 2) this dysregulation was observed in patients experiencing an episode of illness exacerbation, but not in patients studied during a remission phase. Conclusions: A hyperdopaminergic state is present in schizophrenia during the initial episode and subsequent relapses, but not in periods of remission. This finding has important consequences for the development of new treatment strategies for the remission phase.

Magnetic resonance spectroscopy (MRS), an application of the methods of nuclear magnetic resonance (NMR), is a functional imaging modality that provides a view of localized biochemistry in vivo. A number of studies applying MRS to the neurochemistry of schizophrenia have been reported, which encompass a range of patient populations, states of medication, anatomic regions, nuclear species, and MRS techniques. A brief review of the history and methodology of NMR and MRS is presented. Comparison is made of MRS capabilities with other functional imaging modalities. Aspects of the neurochemistry of schizophrenia relevant to MRS studies are reviewed, as are the reported MRS studies involving patients with schizophrenia. Areas of consistent findings include decreased phosphomonoesters and increased phosphodiesters in frontal lobes, and decreases in the putative neuronal cell marker, N-acetylaspartate, in temporal lobes. Studies of neurotransmitters such as glutamate, gamma-aminobutyric acid, and glutamine have generated inconsistent results. New insights into alterations in neurochemistry in schizophrenia have been provided by MRS. Studies of neurotransmitters have future potential with improvements in field strength and in spectral editing techniques. MRS has the potential to measure brain medication levels and simultaneous effects on neurochemistry. MRS may assist in characterizing high-risk populations, and ultimately guide medication use.

In vivo functional brain imaging, including global blood flow, regional cerebral blood flow (rCBF), measured with positron emission tomography (PET) and single photon emission computed tomography (SPECT), and regional cerebral metabolic rate (rCMR) measured with deoxyglucose PET, have been widely used in studies of psychiatric disorders. These studies have found modest differences and required large numbers of patients. Activation studies using rCBF or rCMR as indices of neuronal activity are more sensitive because patients act as their own control; however, findings localize regions of change but provide no data about specific neurotransmitter systems. After a general discussion of the role of neurotransmitter systems in neuropsychiatric disorders, an overview of the methodology of development and selection of radioligands for PET and SPECT is presented. Studies involving PET and SPECT ligand methods are reviewed and their findings summarized, including recent work demonstrating successive mutual modulation of neurotransmitter systems. Kinetic and equilibrium analysis modeling are reviewed. The emerging methodology of measuring neurotransmitter release on activation, both pharmacologically and by task performance, using ligand methods is reviewed and proposed as a promising new approach for studying psychiatric disorders.

Postmortem studies have found evidence of γ-aminobutyric acid (GABA) deficits in fast-spiking, parvalbumin-positive interneurons in the prefrontal cortex in schizophrenia. Magnetic resonance spectroscopy studies in unmedicated patients have reported glutamine or glutamate-glutamine (Glx) elevations in this region. Abnormalities in these transmitters are thought to play a role in cognitive impairments in the illness.To measure GABA and Glx levels in vivo in 2 prefrontal brain regions in unmedicated and medicated patients with schizophrenia and healthy controls.Case-control study.Inpatient psychiatric research unit and associated outpatient clinic.Sixteen unmedicated patients with schizophrenia, 16 medicated patients, and 22 healthy controls matched for age, sex, ethnicity, parental socioeconomic status, and cigarette smoking.Proton magnetic resonance spectroscopy with a 3-T system and the J-edited spin-echo difference method. The GABA and Glx levels were measured in the dorsolateral and medial prefrontal cortex and normalized to the simultaneously acquired water signal. Working memory performance was assessed in all subjects.The GABA and Glx concentrations determined by proton magnetic resonance spectroscopy.In the medial prefrontal cortex region, 30% elevations were found in GABA (P = .02) and Glx (P = .03) levels in unmedicated patients compared with controls. There were no alterations in the medicated patients or in either group in the dorsolateral prefrontal cortex. Both regions showed correlations between GABA and Glx levels in patients and controls. No correlations with working memory performance were found.To our knowledge, this study presents the first GABA concentration measurements in unmedicated patients with schizophrenia, who showed elevations in both GABA and Glx levels in the medial prefrontal cortex but not the dorsolateral prefrontal cortex. Medicated patients did not show these elevations, suggesting possible normalization of levels with antipsychotic medication. The Glx elevations agree with prior magnetic resonance spectroscopy literature, but GABA elevations were unexpected and suggest possible involvement of classes of interneurons not found to show impairments in postmortem studies.

We study the divergent integrals that occur in all post-Newtonian (PN) treatments of radiation reaction in slow-motion, gravitationally bound systems in general relativity. The PN methods implicitly assume that the near-zone metric has a valid asymptotic expansion in powers of the small velocity parameter $\ensuremath{\epsilon}$. We first show explicitly (for the gauge to be used here) that a PN-approximation method leads to a divergent integral at 4-PN order. This divergence arises from the second iteration. Matching arguments are then used to calculate a near-zone term of $O(\mathrm{ln}\ensuremath{\epsilon})$ larger than 4-PN order. On the basis of this calculation and several previous model problems, we argue that the PN divergences signify the breakdown of the PN power-series assumptions, rather than a breakdown of the near and wave zones. Our results suggest that the PN calculations in fact give correct answers at least up to the orders at which divergences appear. The nonanalytic term of $O(\mathrm{ln}\ensuremath{\epsilon})$ beyond 4-PN order arises in the near zone via matching to the wave-zone expansion when we include terms of $O({\ensuremath{\epsilon}}^{3})$ beyond linearized order. We also solve the wave-zone equations at $O({\ensuremath{\epsilon}}^{6})$ beyond linearized order and analyze the inner expansion of the solutions. Matching gives rise to a nonanalytic term in the wave zone at $O({\ensuremath{\epsilon}}^{11}\mathrm{ln}\ensuremath{\epsilon})$, i.e., at $O({\ensuremath{\epsilon}}^{6}\mathrm{ln}\ensuremath{\epsilon})$ beyond linearized order. A straining technique is used in the wave-zone expansion to give a sufficiently accurate approximation to the null surfaces near past and future null infinity. The lowest-order strained solution at first appears to contribute a large, anomalous, time-odd piece to the reaction potential. However, after analyzing the contribution of higher-order wave-zone terms, we obtain agreement with the Burke reaction potential. Our results thus strongly support the usual quadrupole formula.

The Einstein-Maxwell equations are solved for a slowly rotating body with arbitrary charge. The solution is applied to a thin, rotating, charged shell. The angular momentum, gyromagnetic ratio, and other quantities of physical interest are computed. In particular, whenever the charge is less than the mass (but not necessarily small) the gyromagnetic ratio approaches 2 as the shell radius approaches the horizon. Under these conditions the rotational velocity of the inertial frames inside the shell approaches the rotational velocity of the shell. When the charge is greater than the mass there is no horizon and the gyromagnetic ratio can exceed 2. Furthermore, an example is given in which the inertial frames within the shell rotate in a direction opposite that of the shell.

Analytic solutions to Maxwell’s equations in the Schwarzschild geometry are given. These are obtained by differentiating a single superpotential, which is valid (and bounded) at and everywhere outside the gravitational radius. The results have application to black‐hole and neutron‐star electrodynamics.

We demonstrate that when slow-motion infinities arise in an assumed power-series expansion of a time-varying scalar field, they signal the occurrence of terms of logarithmic order in the slow-motion expansion parameter. Previous approximation techniques used in general relativity have assumed that all quantities could be expanded in powers of the small parameter(s). This paper provides the first example, within general relativity, of perturbative effects whose order of magnitude is not a power, but a nonanalytic function of a small parameter. Several previous slow-motion derivations of gravitational radiation damping contained divergent integrals. We first show how an inappropriate expansion method produces divergent integrals in scalar perturbations on a Schwarzschild background. We then use matched asymptotic expansions to discover the aforementioned logarithmic terms. We employ the method of strained coordinates to seek a wave-zone expansion that is uniformly valid at very large distances. We also find that an unexpectedly large, time-odd term in the near zone, which arises via matching to the lowest wave-zone order, is canceled when higher wave-zone orders are considered. No divergent integrals occur. These same techniques will be used in a future paper on the much more complicated gravitational problem.

A new procedure for computing electromagnetic fields in curved space-times is presented. With this procedure, the problem is reduced to solving one complex linear scalar wave equation. Many space-times of astrophysical importance may be treated in this manner, including black-hole and neutron-star spaces and cosmological models.

The causes of the divergent integrals arising in slow-motion expansions of the general relativistic field equations are studied and a remedy for them is suggested. This is done within the context of a model problem involving a coupled nonlinear scalar field and isotropic oscillator. The model is shown to give rise to divergent integrals directly attributable to the nonlinearity when the field is assumed to be analytic in a slowness parameter. Application of a nonregular perturbation approach which includes the method of matched asymptotic expansions is shown to eliminate the infinite contributions.

A model problem designed to incorporate several of the features of slow-motion gravity is analyzed. In common with a previous model calculation the present work supports the idea that divergent integrals which arise in analytic quasistationary perturbation schemes are artifacts of these schemes and can be eliminated by using singular perturbation techniques, in which they get replaced by finite nonanalytic terms. The new features of the present model are (1) it illustrates the necessity of straining the outgoing null coordinate to eliminate logarithmic nonuniformities in nonlinear order for large radius, and (2) it is exactly solvable for the pure-frequency case, which gives an important check on the approximation scheme. Straining the null coordinate immediately introduces time-odd terms in the near zone which are larger than the standard linear-theory damping result. However, these terms are shown to be spurious in that they are canceled by higher-order contributions in the approximation scheme. Thus the standard linear-theory damping result holds in the model, even when nonlinear effects are considered.

We derive the expression for the electromagnetic field of a point charge at rest on the symmetry axis near a rotating Kerr black hole. This is a generalization of the previously obtained solution for the field of a point charge near a nonrotating Schwarzschild black hole. Unlike the Schwarzschild case the charge is found to give rise to magnetic fields as seen by a stationary or locally nonrotating observer.

We present a number of calculations involving the production and propagation of electromagnetic waves in the Schwarzschild metric. They are based on algorithms developed from the power series solutions of the Schwarzschild radial equation (Regge-Wheeler equation) of Arenstorf, Cohen and Kegeles. These include the scattering of electromagnetic plane waves from a Schwarzschild black hole where we find that previous approximate and numerical work is correct and extend those results to higher frequencies and multipolarities. Exact results for the absorption cross-section are presented. We calculate the power radiated from a radially vibrating neutron star and find that the radiation can be hyperemissive. For example, we find for a surface radius of 1.8 Schwarzschild radii the power radiated is enhanced by as much as factor of 3.7, 4.1, 5.1, for dipole, quadrupole and octupole radiation respectively, making electromagnetic radiation a more effective damping mechanism than in flat space. The Schwarzschild radial functions are extensively treated in the appendices and numerical results are presented for various frequencies and radii. A simple asymptotic expansion for one of the connection constants, appropriate for high frequency, is also given.

A slowly rotating black hole is shown to form as a result of gravitational collapse of a dust cloud. The exterior vacuum region is that of the Kerr metric with small rotation parameter at all stages of the collapse; in particular, there is no gravitational radiation. A linearized perturbation of the closed Friedmann-Robertson-Walker dust cloud provides the interior region of the spacetime and matches smoothly to the Kerr exterior. The geometry is shown to be regular on the event horizon. Dragging of inertial frames during the collapse is discussed.

The method of Debye scalar superpotentials has previously been extended by the authors to curved spaces to yield a constructive procedure for neutrino, electromagnetic, and gravitational perturbations of algebraically special spacetimes. The solution of a decoupled scalar wave equation is differentiated to give the solution of the corresponding spinor or tensor perturbation field equations. In this paper covariant formulations and proofs are given. The results are derived in a general spinor formalism framework which extends earlier exterior differential form and tensor treatments of the electromagnetic case.