arXiv subjects

Martin Engman

Publications and source records attributed to Martin Engman.

5 recordsLinked to original sources

arXiv2010

Spectral Geometry of Cosmological and Event Horizons for Kerr-Newman de Sitter metrics

We study the Laplace spectra of the intrinsic instantaneous metrics on the event and cosmological horizons of a Kerr-Newman de Sitter space-time and prove that the spectral data from these horizons uniquely determine the space-time. This is accomplished by exhibiting formulae relating the parameters of the space-time metric to the traces of invariant and equivariant Green's operators associated with these Laplacians. In particular, an interesting explicit formula for the cosmological constant is found.

math-ph↗

arXiv2006

Intrinsic Spectral Geometry of the Kerr-Newman Event Horizon

We uniquely and explicitly reconstruct the instantaneous intrinsic metric of the Kerr-Newman Event Horizon from the spectrum of its Laplacian. In the process we find that the angular momentum parameter, radius, area; and in the uncharged case, mass, can be written in terms of these eigenvalues. In the uncharged case this immediately leads to the unique and explicit determination of the Kerr metric in terms of the spectrum of the event horizon. Robinson's ``no hair" theorem now yields the corollary: One can ``hear the shape" of noncharged stationary axially symmetric black hole space-times by listening to the vibrational frequencies of its event horizon only.

math-ph↗

arXiv2002

A Note on Isometric Embeddings of Surfaces of Revolution

In the special case of S^1 invariant metrics on S^2, we find necessary and sufficient conditions for the existence of isometric embeddings into the canonical R^3, in other words: a Weyl type theorem with converse.

math.DG↗

arXiv1999

The spectrum and isometric embeddings of surfaces of revolution

An upper bound on the first S^1 invariant eigenvalue of the Laplacian for invariant metrics on the 2-sphere is used to find obstructions to the existence of isometric embeddings of such metrics in (R^3,can). As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the surface of revolution cannot be isometrically embedded in (R^3,can). This leads to a generalization of a classical result in the theory of surfaces.

math.DG↗

arXiv1996

Sharp Bounds for Eigenvalues and Multiplicities on Surfaces of Revolution

We find sharp upper bounds for the multiplicities and the numerical values of all the distinct eigenvalues on a surface of revolution diffeomorphic to the sphere.

dg-ga↗