On coupling NEC-violating matter to gravity
Saugata Chatterjee (Department of Physics and Beyond: Center for Fundamental Concepts in Science, Arizona State University, Tempe, AZ, 85287, USA); Maulik Parikh (Department of Physics and Beyond: Center for Fundamental Concepts in Science, Arizona State University, Tempe, AZ, 85287, USA); Jan Pieter van der Schaar (Delta Institute for Theoretical Physics, IOP, GRAPPA, Universiteit van Amsterdam, Science Park 904, Amsterdam, 1090 GL, Netherlands)
We show that effective theories of matter that classically violate the null energy condition cannot be minimally coupled to Einstein gravity without being inconsistent with both string theory and black hole thermodynamics. We argue however that they could still be either non-minimally coupled or coupled to higher-curvature theories of gravity.