7,276 research outputs found

    Gravitating Opposites Attract

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    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+1n+1 (n≄3n \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 Gravit

    An alternative derivation of the gravitomagnetic clock effect

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    The possibility of detecting the gravitomagnetic clock effect using artificial Earth satellites provides the incentive to develop a more intuitive approach to its derivation. We first consider two test electric charges moving on the same circular orbit but in opposite directions in orthogonal electric and magnetic fields and show that the particles take different times in describing a full orbit. The expression for the time difference is completely analogous to that of the general relativistic gravitomagnetic clock effect in the weak-field and slow-motion approximation. The latter is obtained by considering the gravitomagnetic force as a small classical non-central perturbation of the main central Newtonian monopole force. A general expression for the clock effect is given for a spherical orbit with an arbitrary inclination angle. This formula differs from the result of the general relativistic calculations by terms of order c^{-4}.Comment: LaTex2e, 11 pages, 1 figure, IOP macros. Submitted to Classical and Quantum Gravit

    More about Birkhoff's Invariant and Thorne's Hoop Conjecture for Horizons

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    A recent precise formulation of the hoop conjecture in four spacetime dimensions is that the Birkhoff invariant ÎČ\beta (the least maximal length of any sweepout or foliation by circles) of an apparent horizon of energy EE and area AA should satisfy ÎČ≀4πE\beta \le 4 \pi E. This conjecture together with the Cosmic Censorship or Isoperimetric inequality implies that the length ℓ\ell of the shortest non-trivial closed geodesic satisfies ℓ2≀πA\ell^2 \le \pi A. We have tested these conjectures on the horizons of all four-charged rotating black hole solutions of ungauged supergravity theories and find that they always hold. They continue to hold in the the presence of a negative cosmological constant, and for multi-charged rotating solutions in gauged supergravity. Surprisingly, they also hold for the Ernst-Wild static black holes immersed in a magnetic field, which are asymptotic to the Melvin solution. In five spacetime dimensions we define ÎČ\beta as the least maximal area of all sweepouts of the horizon by two-dimensional tori, and find in all cases examined that ÎČ(g)≀16π3E \beta(g) \le \frac{16 \pi}{3} E, which we conjecture holds quiet generally for apparent horizons. In even spacetime dimensions D=2N+2D=2N+2, we find that for sweepouts by the product S1×SD−4S^1 \times S^{D-4}, ÎČ\beta is bounded from above by a certain dimension-dependent multiple of the energy EE. We also find that ℓD−2\ell^{D-2} is bounded from above by a certain dimension-dependent multiple of the horizon area AA. Finally, we show that ℓD−3\ell^{D-3} is bounded from above by a certain dimension-dependent multiple of the energy, for all Kerr-AdS black holes.Comment: 25 page
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