arXiv subjects
Publications and source records attributed to Ivica Smolić.
It is known that the Jebsen-Birkhoff theorem is valid for vacuum solutions to Einstein's equation, as well as some of its generalizations. Using symmetry inheritance properties we investigate in detail the additional constraints that fields have to satisfy in order to allow the Jebsen-Birkhoff theorem in the non-vacuum cases of a wide class of gravitational field equations.
The role of the observers is frequently obscured in the literature, either by writing equations in a coordinate system implicitly pertaining to some specific observer or by entangling the invariance and the observer dependence of physical quantities. Using examples in relativistic kinematics and classical electrodynamics we clarify the confusion underlying these misconceptions.
We study the effects of introducing purely gravitational Chern-Simons Lagrangian terms in ordinary Einstein gravity on stationary rotating black hole solutions and on the associated thermodynamical properties, in a generic number of dimensions which support these terms (i.e. in D = 4k-1). We analyze the conditions, namely the number of vanishing angular momenta, under which the contributions of the Chern-Simons term to the equations of motion and the black hole entropy vanish. The particular case of a 7-dimensional theory in which a purely gravitational Chern-Simons term is added to the Einstein-Hilbert Lagrangian in D=7 dimensions is investigated in some detail. As we have not been able to find exact analytic solutions in nontrivial cases, we turn to perturbation theory and calculate the first-order perturbative correction to the Myers-Perry metric in the case where all angular momenta are equal. The expansion parameter is a dimensionless combination linear in the Chern-Simons coupling constant and the angular momentum. Corrections to horizon and ergosurface properties, as well as black hole entropy and temperature, are presented.
In this note we present a new proof that Killing horizons are equipotential hypersurfaces for the electric and the magnetic scalar potential, that makes no use of gravitational field equations or the assumption about the existence of bifurcation surface.
We show that for general spherically symmetric configurations, contributions of general gravitational and mixed gauge-gravitational Chern-Simons terms to the equations of motion vanish identically in $D>3$ dimensions. This implies that such terms in the action do not affect Birkhoff's theorem or any previously known spherically symmetric solutions. Furthermore, we investigate the thermodynamical properties using the procedure described in an accompanying paper. We find that in $D>3$ static spherically symmetric case Chern-Simons terms do not contribute to the entropy either. Moreover, if one requires only for the metric tensor to be spherically symmetric, letting other fields unrestricted, the results extend almost completely, with only one possible exception --- Chern-Simons Lagrangian terms in which the gravitational part is just the $n=2$ irreducible gravitational Chern-Simons term.
We propose a different approach to the analysis of symmetries in the near-horizon region of black holes. The idea is presented here for spherically symmetric black holes, for which we have shown that the generators of hidden symmetries can be extracted by solving the conformal Killing equation under certain assumptions. Our result is in agreement with that obtained in literature by the analysis of the wave equation in the near-horizon region.
We analyze the problem of defining the black hole entropy when Chern-Simons terms are present in the action. Extending previous works, we define a general procedure, valid in any odd dimensions both for purely gravitational CS terms and for mixed gauge-gravitational ones. The final formula is very similar to Wald's original formula valid for covariant actions, with a significant modification. Notwithstanding an apparent violation of covariance we argue that the entropy formula is indeed covariant.
We review recent results on near-horizon static black hole solutions and entropy in R^2-corrected N=2 SUGRA in D=5, focusing on actions connected to heterotic string compactified on K3\times S^1. Comparison with α'-perturbative results, results obtained by using simple Gauss-Bonnet R^2-correction, OSV conjecture and microscopic stringy description (for small black holes) shows that situation in D=5 is, in a sense, even more interesting then in D=4.
We analyse near-horizon solutions and compare the results for the black hole entropy of five-dimensional spherically symmetric extremal black holes when the N=2 SUGRA actions are supplied with two different types of higher-order corrections: (1) supersymmetric completion of gravitational Chern-Simons term, and (2) Gauss-Bonnet term. We show that for large BPS black holes lowest order α' corrections to the entropy are the same, but for non-BPS are generally different. We pay special attention to the class of prepotentials connected with K3\times T^2 and T^6 compactifications. For supersymmetric correction we find beside BPS also a set of non-BPS solutions. In the particular case of T^6 compactification (equivalent to the heterotic string on $T^4\times S^1$) we find the (almost) complete set of solutions (with exception of some non-BPS small black holes), and show that entropy of small black holes is different from statistical entropy obtained by counting of microstates of heterotic string theory. We also find complete set of solutions for K3\times T^2 and T^6 case when correction is given by Gauss-Bonnet term. Contrary to four-dimensional case, obtained entropy is different from the one with supersymmetric correction. We show that in Gauss-Bonnet case entropy of small ``BPS'' black holes agrees with microscopic entropy in the known cases.