Late-time decay of gravitational and electromagnetic perturbations along the event horizon - art. no. 124005

We study analytically, via the Newman-Penrose formalism the late-time decay of linear electromagnetic and gravitational perturbations along the event horizon (EH) of black holes. We first analyze in detail the case of a Schwa rzschild black here. Using a straightforward local analysis near the EH, we show that, generically, the "ingoing" (s > 0) component of the perturbing field dies off along the EH more rapidly than its "outgoing'' (s < 0) count erpart. Thus, while along r=const>2M lines both components of the perturbat ion admit the well-known t(-2l-3) decay rate, one finds that along the EH t he s < 0 component dies off in advanced time upsilon as upsilon(-2l-3), whe reas the s > 0 component dies off as nu(-2l-4). We then describe the extens ion of this analysis to a Kerr black hole. We conclude that for axially sym metric modes the situation is analogous to the Schwarzschild case. However, for non-axially symmetric modes both s > 0 and s < 0 fields decay at the s ame rate (unlike in the Schwarzschild case). [S0556-2821(99)03422-0].