President Bush (searchremained officially neutral Wednesday in the campaign to recall California Gov. Gray Davis (searchas Arnold Schwarzenegger, a celebrity Republican who had a job in the first Bush administration, entered the race.

But Bush's political advisers were weighing what steps, if any, to take as the California campaign proceeds and calculating the potential impact on Bush's own re-election effort.

The entrance of Schwarzenegger will not affect Bush's two-day trip to Calfornia next week, several administration officials and Bush political advisers said.

Bush is to visit with troops near San Diego, raise money for his campaign and tour the Santa Monica Mountains on Thursday and Friday of next week.

But at least one declared candidate in the recall campaign will be at Bush's fund-raiser in San Diego: Rep. Darrell Issa (search), who financed the recall and who is paying to attend.

News of Schwarzenegger's throwing his hat in stunned some Bush advisers.

But they said Bush maintained his neutral stance in the chaotic race in the nation's most populous state.

"It's a matter for the people of California," said White House spokesman Ken Lisaius.

A Bush political adviser said that the White House viewed the recall campaign as a potential boon to Bush's re-election bid. It is fueling a sharp increase in Republican registrations in the state, this adviser said, speaking on condition of anonymity.

Schwarzenegger headed the first President Bush's Council on Physical Fitness. He does not serve any role in the current Bush administration, officials said. The actor did attend one of Bush's inaugural balls in January 2001.