137 research outputs found
Mass Dependence of the Entropy Product and Sum
For black holes with multiple horizons, the area product of all horizons has
been proven to be mass independent in many cases. Counterexamples were also
found in some occasions. In this paper, we first prove a theorem derived from
the first law of black hole thermodynamics and a mathematical lemma related to
the Vandermonde determinant. With these arguments, we develop some general
criterion for the mass independence of the entropy product as well as the
entropy sum. In particular, if a -dimensional spacetime is spherically
symmetric and its radial metric function is a Laurent series in with
the lowest power and the highest power , we find the criteria is
extremely simple: The entropy product is mass independent if and only if and . The entropy sum is mass independent if and only if and . Compared to previous works, our method does not require an
exact expression of the metric.
Our arguments turn out to be useful even for rotating black holes. By
applying our theorem and lemma to a Myers-Perry black hole with spacetime
dimension , we show that the entropy product/sum is mass independent for all
, while it is mass dependent only for , i.e., the Kerr solution.Comment: 12 page
Universality of BSW mechanism for spinning particles
Ba\~nados (BSW) found that Kerr black holes can act as particle
accelerators with collisions at arbitrarily high center-of-mass energies.
Recently, collisions of particles with spin around some rotating black holes
have been discussed. In this paper, we study the BSW mechanism for spinning
particles by using a metric ansatz which describes a general rotating black
hole. We notice that there are two inequivalent definitions of center-of-mass
(CM) energy for spinning particles. We mainly discuss the CM energy defined in
terms of the worldline of the particle. We show that there exists an
energy-angular momentum relation that causes collisions with
arbitrarily high energy near-extremal black holes. We also provide a simple but
rigorous proof that the BSW mechanism breaks down for nonextremal black holes.
For the alternative definition of the CM energy, some authors find a new
critical spin relation that also causes the divergence of the CM mass. However,
by checking the timelike constraint, we show that particles with this critical
spin cannot reach the horizon of the black hole. Further numerical calculation
suggests that such particles cannot exist anywhere outside the horizon. Our
results are universal, independent of the underlying theories of gravity.Comment: 8 pages, 1 figure
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