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R. B. Mann

Publications and source records attributed to R. B. Mann.

At least 127 records · Page 7Linked to original sources
arXiv1999

Exact Solutions of Relativistic Two-Body Motion in Lineal Gravity

We develop the canonical formalism for a system of $N$ bodies in lineal gravity and obtain exact solutions to the equations of motion for N=2. The determining equation of the Hamiltonian is derived in the form of a transcendental equation, which leads to the exact Hamiltonian to infinite order of the gravitational coupling constant. In the equal mass case explicit expressions of the trajectories of the particles are given as the functions of the proper time, which show characteristic features of the motion depending on the strength of gravity (mass) and the magnitude and sign of the cosmological constant. As expected, we find that a positive cosmological constant has a repulsive effect on the motion, while a negative one has an attractive effect. However, some surprising features emerge that are absent for vanishing cosmological constant. For a certain range of the negative cosmological constant the motion shows a double maximum behavior as a combined result of an induced momentum-dependent cosmological potential and the gravitational attraction between the particles. For a positive cosmological constant, not only bounded motions but also unbounded ones are realized. The change of the metric along the movement of the particles is also exactly derived.

gr-qc↗
arXiv1999

Entropy of Rotating Misner String Spacetimes

Using a boundary counterterm prescription motivated by the AdS/CFT conjecture, I evaluate the energy, entropy and angular momentum of the class of Kerr-NUT/bolt-AdS spacetimes. As in the non-rotating case, when the NUT charge is nonzero the entropy is no longer equal to one-quarter of the area due to the presence of the Misner string. When the cosmological constant is also non-zero, the entropy is bounded from above.

hep-th↗
arXiv1999

Misner String Entropy

I show that gravitational entropy can be ascribed to spacetimes containing Misner strings (the gravitational analogues of Dirac strings), even in the absence of any other event horizon (or bolt) structures. This result follows from an extension of proposals for evaluating the stress-energy of a gravitational system which are motivated by the AdS/CFT correspondence.

hep-th↗
arXiv1999

Exact Relativistic Two-Body Motion in Lineal Gravity

We consider the N-body problem in (1+1) dimensional lineal gravity. For 2 point masses (N=2) we obtain an exact solution for the relativistic motion. In the equal mass case we obtain an explicit expression for their proper separation as a function of their mutual proper time. Our solution gives the exact Hamiltonian to infinite order in the gravitational coupling constant.

gr-qc↗
arXiv1999

Cosmological Pair Production of Charged and Rotating Black Holes

We investigate the general process of black hole pair creation in a cosmological background, considering the creation of charged and rotating black holes. We motivate the use of Kerr-Newmann-deSitter solutions to investigate this process, showing how they arise from more general C-metric type solutions that describe a pair of general black holes accelerating away from each other in a cosmological background. All possible KNdS-type spacetimes are classified and we examine whether they may be considered to be in full thermodynamic equilibrium. Instantons that mediate the creation of these space-times are constructed and we see that they are necessarily complex due to regularity requirements. Thus we argue that instantons need not always be real Euclidean solutions to the Einstein equations. Finally, we calculate the actions of these instantons and find that the standard action functional must be modified to correctly take into account the effects of the rotation. The resultant probabilities for the creation of the space-times are found to be real and consistent with the interpretation that the entropy of a charged and rotating black hole is the logarithm of the number of its quantum states.

gr-qc↗
arXiv1999

Moving Observers, Non-orthogonal Boundaries, and Quasilocal Energies

The popular Hamilton-Jacobi method first proposed by Brown and York for defining quasilocal quantities such as energy for spatially bound regions assumes that the spatial boundary is orthogonal to the foliation of the spacetime. Such a restriction is undesirable for both theoretical and computational reasons. We remove the orthogonality assumption and show that it is more natural to focus on the foliation of the spatial boundary rather than the foliation of the entire spatially bound region. Reference spacetimes which define additional terms in the action are discussed in detail. To demonstrate this new formulation, we calculate the quasilocal energies seen by observers who are moving with respect to a Schwarzschild black hole.

gr-qc↗
arXiv1999

Gravity From Topological Field Theory

We construct a topological field theory which, on the one hand, generalizes BF theories in that there is non-trivial coupling to `topological matter fields'; and, on the other, generalizes the three-dimensional model of Carlip and Gegenberg to arbitrary dimensional manifolds. Like the three dimensional model, the theory can be considered to describe a gravitational field interacting with topological matter. In particular, in two dimensions, the model is that of gravity on a torus. In four dimensions, the model is shown to admit constant curvature black hole solutions.

hep-th↗
arXiv1998

Complex Instantons and Charged Rotating Black Hole Pair Creation

We consider the general process of pair-creation of charged rotating black holes. We find that instantons which describe this process are necessarily complex due to regularity requirements. However their associated probabilities are real, and fully consistent with the interpretation that the entropy of a charged rotating black hole is the logarithm of the number of its quantum states.

gr-qc↗
arXiv1998

Cosmological Supergravity from a Massive Superparticle and Super Cosmological Black Holes

We describe in superspace a classical theory of two dimensional $(1,1)$ dilaton supergravity with a cosmological constant, both with and without coupling to a massive superparticle. We give general exact non-trivial superspace solutions for the compensator superfield that describes the supergravity in both cases. We then use these compensator solutions to construct models of two-dimensional supersymmetric cosmological black holes.

hep-th↗
arXiv1998

Stable central structures in topologically nontrivial Anti-de Sitter spacetimes

We investigate stable central structures in multiply-connected, anti de Sitter spacetimes with spherical, planar and hyperbolic geometries. We obtain an exact solution for the pressure in terms of the radius when the density is constant. We find that, apart from the usual simply-connected spherically symmetric star with a well-behaved metric at $r=0$, the only solutions with non-singular pressure and density have a wormhole topology. However these wormhole solutions must be composed of matter which violates the weak energy condition. Admitting this type of matter, we obtain a structure which is maintained via a balance between its cohesive tension and its repulsive negative matter density. If the tension is insufficiently large, this structure can collapse to a black hole of negative mass.

gr-qc↗
arXiv1998

A New Approach to Black Hole Microstates

If one encodes the gravitational degrees of freedom in an orthonormal frame field there is a very natural first order action one can write down (which in four dimensions is known as the Goldberg action). In this essay we will show that this action contains a boundary action for certain microscopic degrees of freedom living at the horizon of a black hole, and argue that these degrees of freedom hold great promise for explaining the microstates responsible for black hole entropy, in any number of spacetime dimensions. This approach faces many interesting challenges, both technical and conceptual.

gr-qc↗
arXiv1998

Test of Special Relativity and Equivalence principle from K Physics

A violation of Local Lorentz Invariance (VLI) and hence the special theory of relativity or a violation of equivalence principle (VEP) in the Kaon system can, in principle, induce oscillations between $K^0$ and $\bar{K}^0$. We construct a general formulation in which simultaneous pairwise diagonalization of mass, momemtum, weak or gravitational eigenstates is not assumed. %and the maximum attainable %velocities of the velocity eigenstates are different. We discuss this problem in a general way and point out that, as expected, the VEP and VLI contributions are indistinguishable. We then insist on the fact that VEP or VLI can occur even when CPT is conserved. A possible CP violation of the superweak type induced by VEP or VLI is introduced and discussed. We show that the general VEP mechanism (or the VLI mechanism, but not both simultaneously), with or without conserved CPT, could be clearly tested experimentally through the energy dependence of the $K_L-K_S$ mass difference and of $η_{+-}$, $η_{00}$, $δ$. Constraints imposed by present experiments are calculated.

hep-ph↗
arXiv1998

Super Black Hole from Cosmological Supergravity with a Massive Superparticle

We describe in superspace a classical theory of two dimensional $(1,1)$ cosmological dilaton supergravity coupled to a massive superparticle. We give an exact non-trivial superspace solution for the compensator superfield that describes the supergravity, and then use this solution to construct a model of a two-dimensional supersymmetric black hole.

hep-th↗
arXiv1997

Cosmological Pair Creation of Charged and Rotating Black Holes

In this paper, we investigate the pair creation of charged and rotating black hole pairs in a background with a positive cosmological constant. Instantons to describe this situation are constructed from the Kerr-Newmann deSitter solutions to the Einstein-Maxwell equations and the actions of these instantons are calculated in order to estimate pair creation rates and the entropy of the created spacetimes.

gr-qc↗
arXiv1997

Palatini Variational Principle for an Extended Einstein-Hilbert Action

We consider a Palatini variation on a generalized Einstein-Hilbert action. We find that the Hilbert constraint, that the connection equals the Christoffel symbol, arises only as a special case of this general action, while for particular values of the coefficients of this generalized action, the connection is completely unconstrained. We discuss the relationship between this situation and that usually encountered in the Palatini formulation.

gr-qc↗
arXiv1997

Palatini Variational Principle for $N$-Dimensional Dilaton Gravity

We consider a Palatini variation on a general $N$-Dimensional second order, torsion-free dilaton gravity action and determine the resulting equations of motion. Consistency is checked by considering the restraint imposed due to invariance of the matter action under simple coordinate transformations, and the special case of N=2 is examined. We also examine a sub-class of theories whereby a Palatini variation dynamically coincides with that of the "ordinary" Hilbert variational principle; in particular we examine a generalized Brans-Dicke theory and the associated role of conformal transformations.

gr-qc↗
arXiv1997

Test of Special Relativity from K Physics

A breakdown of the Local Lorentz Invariance and hence the special theory of relativity in the Kaon system can, in principle, induce oscillations between the $K^0$ and $\bar{K}^0$ states. We construct a general formulation in which simultaneous pairwise diagonalization of mass, momentum and weak eigenstates is not assumed and the maximum attainable speeds of the momentum eigenstates are different. This mechanism permits Local Lorentz Invariance violation in a manner that may or may not violate CPT. In the $CPT-$conserving case, we show that violation of special relativity could be clearly tested experimentally via the energy dependence of the $K_L-K_S$ mass difference and we discuss constraints imposed by present experiments. In the CPT-violating case the $K^0$--$\bar{K}^0$ system also allows the possiblity of testing different Lorentz properties of matter and antimatter.

hep-ph↗