It is shown that the problem of the existence of a time function or of a semi-time function in general relativity is mathematically equivalent to that of the existence of a continuous utility function for an agent in microeconomics. Some theorems developed in economics can therefore be used in general relativity. With this strategy it is possible to give a new proof that stable causality is equivalent to the existence of a time function and also to clarify in which circumstances the causal structure can be recovered from the set of time functions allowed by the spacetime.
Time functions as utility functions / E. Minguzzi. - STAMPA. - 49:(2011), pp. 97-104. (Intervento presentato al convegno Advances in Lorentzian geometry tenutosi a Berlino nel 18-20 novembre 2008).
Time functions as utility functions
MINGUZZI, ETTORE
2011
Abstract
It is shown that the problem of the existence of a time function or of a semi-time function in general relativity is mathematically equivalent to that of the existence of a continuous utility function for an agent in microeconomics. Some theorems developed in economics can therefore be used in general relativity. With this strategy it is possible to give a new proof that stable causality is equivalent to the existence of a time function and also to clarify in which circumstances the causal structure can be recovered from the set of time functions allowed by the spacetime.
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