Surface Gravity of Dynamical Horizons: A Causal Perspective

We consider marginally trapped surfaces in a spherically symmetric spacetime evolving due to the presence of a perfect fluid in D-dimensions and look at the various definitions of the surface gravity for these marginally trapped surfaces. We show that using Einstein equations it is possible to simplify and obtain general formulae for the surface gravity in terms of invariant quantities defined at these marginally trapped surfaces like area radius, cosmological constant and principal values of the energy-momentum tensor \r{ho}, p. We then correlate these expressions of surface gravity to the cases of dynamical horizons and timelike tubes and find which proposals of surface gravity are causally sensitive as these surfaces undergo causal transitions from spacelike to timelike and vice versa.