Extending the isolated horizon phase space to string-inspired gravity models

Liko, Tomas (2008) Extending the isolated horizon phase space to string-inspired gravity models. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

An isolated horizon (IH) is a null hypersurface at which the geometry is held fixed. This generalizes the notion of an event horizon so that the black hole is an object that is in local equilibrium with its (possibly) dynamic environment. The first law of IH mechanics that arises from the framework relates quantities that are all defined at the horizon. -- IHs have been extensively studied in Einstein gravity with various matter couplings and rotation, and in asymptotically flat and asymptotically anti-de Sitter (ADS) spacetimes in all dimensions D ≥ 3. Motivated by the nonuniqueness of black holes in higher dimensions and by the black-hole/string correspondence principle, we devote this thesis to the extension of the framework to include IHs in string-inspired gravity models, specifically to Einstein-Maxwell-Chern-Simons (EM-CS) theory and to Einstein-Gauss-Bonnet (EGB) theory in higher dimensions. The focus is on determining the generic features of black holes that are solutions to the field equations of the theories under consideration. To this end, we construct a covariant phase space for both theories; this allows us to prove that the corresponding weakly IHs (WIHs) satisfy the zeroth and first laws of black-hole mechanics. -- For EM-CS theory, we find that in the limit when the surface gravity of the horizon goes to zero there is a topological constraint. Specifically, the integral of the scalar curvature of the cross sections of the horizon has to be positive when the dominant energy condition is satisfied and the cosmological constant Λ is zero or positive. There is no constraint on the topology of the horizon cross sections when Λ < 0. These results on topology of IHs are independent of the material content of the stress-energy tensor, and therefore the conclusions for EM-CS theory carry over to theories with arbitrary matter fields (minimally) coupled to Einstein gravity. -- In addition, we consider rotating IHs in asymptotically ADS and flat spacetimes, and find the restrictions that are imposed on them if one assumes they are supersymmetric. For the existence of a null Killing spinor in four-dimensional N = 2 gauged supergravity we show that ADS supersymmetric isolated horizons (SIHs) are necessarily extremal, that rotating SIHs must have non-trivial electromagnetic fields, and that non-rotating SIHs necessarily have constant curvature horizon cross sections and a magnetic (though not electric) charge. When the cosmological constant is zero then the gravitational angular momentum vanishes identically and the corresponding SIHs are strictly non-rotating. Likewise for the existence of a null Killing spinor in five-dimensional N = 1 supergravity, we show that SIHs (in asymptotically flat spacetimes) are strictly non-rotating and extremal. -- For EGB theory we restrict our study to non-rotating WIHs and show explicitly that the expression for the entropy appearing in the first law is in agreement with those predicted by the Euclidean and Noether charge methods. By carefully examining a concrete example of two Schwarzschild black holes in a flat four-dimensional spacetime that are merging, we find that the area-increase law can be violated for certain values of the GB parameter. This provides a constraint on the free parameter.

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